https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Maxim&feedformat=atomUW-Math Wiki - User contributions [en]2020-09-29T03:32:38ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20017Graduate/Postdoc Topology and Singularities Seminar2020-09-28T21:33:36Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | recording<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|[https://uwmadison.box.com/v/SingularitiesElduque Zoom]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20013Graduate/Postdoc Topology and Singularities Seminar2020-09-28T19:12:58Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | recording<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|[https://uwmadison.box.com/s/9xp1c3uodi5th37p81z9gbz3st9qpm1y Zoom]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20012Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:53:53Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | recording<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|[ Zoom]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20011Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:43:17Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | recording<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|[https://uwmadison.zoom.us/rec/share/1RrQfjMQ0tqMpx0g8fscNAWPE8ebJ0FSUAk9yxi2IxTT4VWeJYqtrY8PbM1O41o.N7mBl516TlmqGV1a?startTime=1601304771000 Zoom]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20010Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:41:21Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | recording<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20009Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:40:05Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20008Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:39:32Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules] [https://uwmadison.zoom.us/rec/share/1RrQfjMQ0tqMpx0g8fscNAWPE8ebJ0FSUAk9yxi2IxTT4VWeJYqtrY8PbM1O41o.N7mBl516TlmqGV1a?startTime=1601304771000 (recording)]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20007Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:38:27Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20006Graduate/Postdoc Topology and Singularities Seminar2020-09-28T18:37:41Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules <a href="https://uwmadison.zoom.us/rec/share/1RrQfjMQ0tqMpx0g8fscNAWPE8ebJ0FSUAk9yxi2IxTT4VWeJYqtrY8PbM1O41o.N7mBl516TlmqGV1a?startTime=1601304771000">recording</a>]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=20003Geometry and Topology2020-09-28T02:16:33Z<p>Maxim: /* Seminars */</p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
[[Graduate/Postdoc Topology and Singularities Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[https://www.math.wisc.edu/~gchen/ Gao Chen] (Stony Brook 2017) <br />
Complex geometry, quaternionic geometry and octonionic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
Shaosai Huang (Stony Brook 2018)<br />
Ricci flows<br />
<br />
[https://brainhelper.wordpress.com/ Brian Hepler] (Northeastern U 2019)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing19.html Singularities in the Midwest, VI]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest, V]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=20002Graduate/Postdoc Topology and Singularities Seminar2020-09-28T02:12:28Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu'''). We plan to have all talks recorded.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Topology_and_Singularities_Seminar&diff=20001Topology and Singularities Seminar2020-09-28T02:11:00Z<p>Maxim: Created page with "See: https://www.math.wisc.edu/wiki/index.php/Graduate/Postdoc_Topology_and_Singularities_Seminar"</p>
<hr />
<div>See: https://www.math.wisc.edu/wiki/index.php/Graduate/Postdoc_Topology_and_Singularities_Seminar</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=20000Main Page2020-09-28T02:09:46Z<p>Maxim: /* Math Seminars at UW-Madison */</p>
<hr />
<div><br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone. <br />
<br />
*[[Getting Around Van Vleck]]<br />
<br />
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<br />
== Math Seminars at UW-Madison ==<br />
<br />
*[[Colloquia|Colloquium]]<br />
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=== Graduate Student Seminars ===<br />
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=== Other ===<br />
*[https://sites.google.com/site/uwmadisondrp/home Directed Reading Program]<br />
*[[Madison Math Circle]]<br />
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*[http://www.siam-uw.org/ UW-Madison SIAM Student Chapter]<br />
*[http://www.math.wisc.edu/%7Emathclub/ UW-Madison Math Club]<br />
*[[Putnam Club]]<br />
*[[Undergraduate Math Competition]]<br />
*[[Basic Linux Seminar]]<br />
*[[Basic HTML Seminar]]<br />
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== Graduate Program ==<br />
<br />
* [[Algebra Qualifying Exam]]<br />
* [[Analysis Qualifying Exam]]<br />
* [[Topology Qualifying Exam]]<br />
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== Undergraduate Program ==<br />
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* [[Overview of the undergraduate math program|Overview]]<br />
* [[Groups looking to hire students as tutors]]<br />
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== Getting started with Wiki-stuff ==<br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
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* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19999Graduate/Postdoc Topology and Singularities Seminar2020-09-27T23:56:58Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu''').<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|[https://www.math.brown.edu/~jusatine/ Jeremy Usatine (Brown)]<br />
|[[#Jeremy Usatine|TBA]]<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19998Graduate/Postdoc Topology and Singularities Seminar2020-09-27T18:32:53Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu''').<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19997Graduate/Postdoc Topology and Singularities Seminar2020-09-27T18:32:02Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu''').<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano(U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|[https://sites.google.com/prod/view/feng-hao/home Feng Hao (Leuven)] <br />
|[[#Feng Hao|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19996Graduate/Postdoc Topology and Singularities Seminar2020-09-27T18:29:15Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu''').<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano(U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|Feb 1<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Feb 8<br />
|Feng Hao (Leuven) <br />
|TBA<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19963Graduate/Postdoc Topology and Singularities Seminar2020-09-25T16:48:32Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
(or, if you get an error message, just email '''maxim@math.wisc.edu''').<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano(U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19954Graduate/Postdoc Topology and Singularities Seminar2020-09-24T21:51:28Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b>2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano(U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19953Graduate/Postdoc Topology and Singularities Seminar2020-09-24T21:51:14Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b> 2 PM</b>)<br />
|[https://lsa.umich.edu/math/people/postdoc-faculty/olano.html Sebastián Olano(U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19952Graduate/Postdoc Topology and Singularities Seminar2020-09-24T21:47:24Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 (<b> 2 PM</b><br />
|[Sebastián Olano (U Michigan-Ann Arbor)] <br />
|[[#Sebastián Olano|TBA]]<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19944Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:34:47Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|TBA<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19942Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:33:28Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|[https://sites.google.com/site/yongqiangliuted/ Yongqiang Liu (USTC, China)] <br />
|[[#Yongqiang Liu|TBA]]<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|[https://palmiron.wordpress.com/ Patricio Almirón Cuadros (Madrid)]<br />
|[[#Patricio Almirón Cuadros|TBA]]<br />
|-<br />
|-<br />
|Nov 30<br />
|[http://www.bcamath.org/en/people/jbobadilla Javier Fernandez de Bobadilla (Bilbao)] <br />
|[[#Javier Fernandez de Bobadilla|TBA]]<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|[http://www.bcamath.org/en/people/ipallares Irma Pallarés Torres (Bilbao)] <br />
|[[#Irma Pallarés Torres|TBA]]<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19941Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:29:46Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 19<br />
|[https://brainhelper.wordpress.com/ Brian Hepler (UW-Madison)]<br />
|[[#Brian Hepler|TBA]]<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19940Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:28:10Z<p>Maxim: /* Abstracts */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
===Yongqiang Liu===<br />
<br />
'''Title'''<br />
<br />
Abstract:<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19939Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:27:25Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eva Elduque===<br />
<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19938Graduate/Postdoc Topology and Singularities Seminar2020-09-23T23:25:14Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|[https://sites.google.com/site/evaelduque/ Eva Elduque (U Michigan-Ann Arbor)]<br />
|[[#Eva Elduque|Mixed Hodge structures on Alexander modules]]<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
'''Mixed Hodge structures on Alexander modules'''<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19935Graduate/Postdoc Topology and Singularities Seminar2020-09-23T15:28:54Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: '''join-singularities@lists.wisc.edu'''<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19934Graduate/Postdoc Topology and Singularities Seminar2020-09-23T15:28:07Z<p>Maxim: /* Fall 2020 / Spring 2021 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28. Future seminar announcements will be sent to the "singularities" mailing list. To subscribe, please send an email at: join-singularities@lists.wisc.edu<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19933Graduate/Postdoc Topology and Singularities Seminar2020-09-23T14:41:48Z<p>Maxim: /* Fall 2020 */</p>
<hr />
<div><br />
== Fall 2020 / Spring 2021 ==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Jan 25<br />
|Irma Pallarés Torres (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19928Graduate/Postdoc Topology and Singularities Seminar2020-09-22T14:42:28Z<p>Maxim: /* Fall 2020 */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 14<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19927Graduate/Postdoc Topology and Singularities Seminar2020-09-22T14:17:18Z<p>Maxim: /* Fall 2020 */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|Javier Fernandez de Bobadilla (Bilbao) <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19926Graduate/Postdoc Topology and Singularities Seminar2020-09-22T14:08:40Z<p>Maxim: /* Fall 2020 */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón Cuadros (Madrid)<br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19925Graduate/Postdoc Topology and Singularities Seminar2020-09-22T14:01:09Z<p>Maxim: /* Fall 2020 */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|Patricio Almirón <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19924Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:36:38Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
<i>Mixed Hodge structures on Alexander modules</i><br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19923Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:35:54Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
Mixed Hodge structures on Alexander modules<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19922Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:35:38Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
Mixed Hodge structures on Alexander modules<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&ast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19921Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:34:54Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
Mixed Hodge structures on Alexander modules<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>&lowast;</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>&lowast;</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19919Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:34:33Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
Mixed Hodge structures on Alexander modules<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>&lowast;</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>*</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>*</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the map &fnof;. In this talk, we will discuss how to equip the torsion part of the Alexander modules (with respect to the &#90;-actions) with canonical mixed Hodge structures. Since &#85;<sup>&fnof;</sup> is not an algebraic variety in general, these mixed Hodge structures cannot be obtained from Deligne's theory. The resulting mixed Hodge structures on Alexander modules have some desirable properties. For example, the covering space map &#85;<sup>&fnof;</sup> &rarr; &#85; induces morphisms of mixed Hodge structures in homology, where the homology of &#85; is equipped with Deligne's mixed Hodge structure. We will explore several consequences/applications of this fact, regarding weights and semisimplicity. We will also compare the mixed Hodge structures on Alexander modules to other well studied mixed Hodge structures in the literature, including the limit mixed Hodge structure on the generic fiber of &fnof;. Joint work with C. Geske, M. Herradón Cueto, L. Maxim, and B. Wang.<br />
<br />
==== Oct 5: Yongqiang Liu====<br />
Title<br />
<br />
Abstract<br />
<br />
== Fall 2018==<br />
<br />
The Seminar meets at 10.30 to 11:30 on Fridays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 5<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant"<br />
|-<br />
|-<br />
|Oct 26<br />
|Fenglin Li<br />
|"Hasse principle and u-invariant (II)"<br />
|-<br />
|-<br />
|Nov 2<br />
|José Rodríguez<br />
|"Maximum likelihood degree"<br />
|-<br />
|}<br />
=== Abstracts ===<br />
<br />
<br />
==== Nov 2: José Rodríguez====<br />
Maximum likelihood degree<br />
<br />
In statistics, point estimation uses sample data to calculate the "best estimate" of an unknown population parameter. For example, the sample average can be used to estimate the population mean. While there are many different point estimators, some of the most common ones are the maximum likelihood estimator (MLE), method of moments, and generalized method of moments (GMM).<br />
<br />
In algebraic statistics statistical models are studied through the lens of algebra, geometry, and combinatorics. From model selection to inference, this interdisciplinary field has seen applications in a wide range of statistical procedures. In this talk, I will review maximum likelihood estimation and the maximum likelihood degree (ML degree) for discrete models. In particular, I will discuss how the ML degree gives a measure of algebraic complexity of the point estimate for MLE and how we can compute it using tools from topology and geometry. If time permits I will also discuss how we can use maximum likelihood degrees to study singularities.<br />
<br />
== Fall 2017==<br />
<br />
The Seminar meets at 3:30 to 4:30 pm on Wednesdays in Van Vleck 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Oct 4<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (I)"<br />
|-<br />
|-<br />
|Oct 11<br />
|Eva Elduque <br />
|"Twisted Alexander Modules of Complex Essential Hyperplane Arrangement Complements (II)"<br />
|-<br />
|-<br />
|Oct 18<br />
|Sebastian Baader <br />
|"Dehn twist length in mapping class groups"<br />
|-<br />
|-<br />
|Oct 25<br />
|Cancelled <br />
|-<br />
|-<br />
|Nov 1<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (I)"<br />
|-<br />
|-<br />
|Nov 8<br />
|Christian Geske <br />
|"Algebraic Intersection Spaces (II)"<br />
|-<br />
|-<br />
|Nov 15<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (I)"<br />
|-<br />
|-<br />
|Nov 22<br />
| Thanksgiving break<br />
|<br />
|-<br />
|-<br />
|Nov 29<br />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|December 6<br />
|Alexandra Kjuchukova <br />
|"Singular branched covers of four-manifolds and applications"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=19917Graduate/Postdoc Topology and Singularities Seminar2020-09-22T03:32:43Z<p>Maxim: /* Sept 28: Eva Elduque */</p>
<hr />
<div><br />
== Fall 2020==<br />
<br />
This semester the seminar is on Zoom, hosted by Laurentiu Maxim and Botong Wang. The meeting information is below. We meet on Mondays, at 10am, starting on September 28.<br />
<br />
Topic: Topology and Singularities Seminar<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/92348710211?pwd=TWlEWlE4K0RiTDVjRUhKZW9VV0p4QT09<br />
<br />
Meeting ID: 923 4871 0211<br />
<br />
Passcode: 752425<br />
<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept 28<br />
|Eva Elduque (U Michigan-Ann Arbor)<br />
|"Mixed Hodge structures on Alexander modules"<br />
|-<br />
|-<br />
|Oct 5<br />
|Yongqiang Liu (USTC, China) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 12<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 19<br />
|Brian Hepler (UW-Madison) <br />
|"TBA"<br />
|-<br />
|-<br />
|Oct 26 <br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 2<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 9<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 16<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Nov 30<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|Dec 7<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|}<br />
<br />
=== Abstracts ===<br />
<br />
<br />
==== Sept 28: Eva Elduque====<br />
Mixed Hodge structures on Alexander modules<br />
<br />
Abstract: Let &fnof; : &#85; &rarr; &#67;<sup>*</sup> be an algebraic map from a smooth complex connected algebraic variety &#85; to the punctured complex line &#67;<sup>*</sup>. Using &fnof; to pull back the exponential map &#67; &rarr; &#67;<sup>*</sup>, one obtains an infinite cyclic cover &#85;<sup>&fnof;</sup> of the variety &#85;. The homology groups of this infinite cyclic cover, which are endowed with &#90;-actions by deck transformations, determine the family of Alexander modules associated to the ma