https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Kjuchukova&feedformat=atomUW-Math Wiki - User contributions [en]2021-02-26T08:37:14ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14654Graduate/Postdoc Topology and Singularities Seminar2017-12-05T21:56:20Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>== 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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14381Graduate/Postdoc Topology and Singularities Seminar2017-10-17T14:13:08Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>== 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 />
== 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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14280Geometry and Topology Seminar 2019-20202017-10-02T19:01:17Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|Jiyuan Han (University of Wisconsin-Madison)<br />
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]<br />
|Local <br />
|-<br />
|September 22<br />
|Sigurd Angenent (UW-Madison)<br />
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]<br />
|Local<br />
|-<br />
|September 29<br />
|Ke Zhu (Minnesota State University)<br />
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]<br />
|Bing Wang<br />
|-<br />
|October 6<br />
|Shaosai Huang (Stony Brook)<br />
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|Sebastian Baader (Bern)<br />
|[[#Sebastian Baader| "A filtration of the Gordian complex via symmetric groups"]]<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|Brian Hepler (Northeastern University)<br />
|TBA<br />
|Max<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Sebastian Baader ===<br />
"A filtration of the Gordian complex via symmetric groups"<br />
<br />
The Gordian complex is a countable graph whose vertices correspond to knot types and whose edges correspond to pairs of knots that are related by a crossing change in a suitable diagram. For every natural number n, we consider the subgraph of the Gordian complex defined by restricting to the knot types whose fundamental group surjects onto S_n. We will prove that the various inclusion maps from these subgraphs into the Gordian complex are isometric embeddings. From this, we obtain a simple metric filtration of the Gordian complex.<br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14279Geometry and Topology Seminar 2019-20202017-10-02T19:00:26Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|Jiyuan Han (University of Wisconsin-Madison)<br />
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]<br />
|Local <br />
|-<br />
|September 22<br />
|Sigurd Angenent (UW-Madison)<br />
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]<br />
|Local<br />
|-<br />
|September 29<br />
|Ke Zhu (Minnesota State University)<br />
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]<br />
|Bing Wang<br />
|-<br />
|October 6<br />
|Shaosai Huang (Stony Brook)<br />
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|Sebastian Baader (Bern)<br />
|[[#Sebastian Baader| A filtration of the Gordian complex via symmetric groups]<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|Brian Hepler (Northeastern University)<br />
|TBA<br />
|Max<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Sebastian Baader ===<br />
"A filtration of the Gordian complex via symmetric groups"<br />
<br />
The Gordian complex is a countable graph whose vertices correspond to knot types and whose edges correspond to pairs of knots that are related by a crossing change in a suitable diagram. For every natural number n, we consider the subgraph of the Gordian complex defined by restricting to the knot types whose fundamental group surjects onto S_n. We will prove that the various inclusion maps from these subgraphs into the Gordian complex are isometric embeddings. From this, we obtain a simple metric filtration of the Gordian complex.<br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14278Geometry and Topology Seminar 2019-20202017-10-02T18:59:17Z<p>Kjuchukova: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|Jiyuan Han (University of Wisconsin-Madison)<br />
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]<br />
|Local <br />
|-<br />
|September 22<br />
|Sigurd Angenent (UW-Madison)<br />
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]<br />
|Local<br />
|-<br />
|September 29<br />
|Ke Zhu (Minnesota State University)<br />
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]<br />
|Bing Wang<br />
|-<br />
|October 6<br />
|Shaosai Huang (Stony Brook)<br />
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|Sebastian Baader (Bern)<br />
|A filtration of the Gordian complex via symmetric groups<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|Brian Hepler (Northeastern University)<br />
|TBA<br />
|Max<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Sebastian Baader ===<br />
"A filtration of the Gordian complex via symmetric groups"<br />
<br />
The Gordian complex is a countable graph whose vertices correspond to knot types and whose edges correspond to pairs of knots that are related by a crossing change in a suitable diagram. For every natural number n, we consider the subgraph of the Gordian complex defined by restricting to the knot types whose fundamental group surjects onto S_n. We will prove that the various inclusion maps from these subgraphs into the Gordian complex are isometric embeddings. From this, we obtain a simple metric filtration of the Gordian complex.<br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14277Geometry and Topology Seminar 2019-20202017-10-02T18:57:57Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|Jiyuan Han (University of Wisconsin-Madison)<br />
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]<br />
|Local <br />
|-<br />
|September 22<br />
|Sigurd Angenent (UW-Madison)<br />
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]<br />
|Local<br />
|-<br />
|September 29<br />
|Ke Zhu (Minnesota State University)<br />
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]<br />
|Bing Wang<br />
|-<br />
|October 6<br />
|Shaosai Huang (Stony Brook)<br />
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|Sebastian Baader (Bern)<br />
|A filtration of the Gordian complex via symmetric groups<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|Brian Hepler (Northeastern University)<br />
|TBA<br />
|Max<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2017&diff=14205Algebraic Geometry Seminar Fall 20172017-09-22T16:11:04Z<p>Kjuchukova: /* Fall 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B321.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--and for [[Algebraic Geometry Seminar Spring 2017 | the next semester]].---><br />
<!-- and for [[Algebraic Geometry Seminar | this semester]].---><br />
<br />
==Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2017 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|October 6<br />
|[http://www.math.wisc.edu/~mkbrown5// Michael Brown (UW-Madison)] <br />
|[[#Michael Brown|Topological K-theory of equivariant singularity categories]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Michael Brown===<br />
<br />
'''Topological K-theory of equivariant singularity categories'''<br />
<br />
This is joint work with Tobias Dyckerhoff. Topological K-theory of complex-linear dg categories is a notion introduced by Blanc in his recent article "Topological K-theory of complex noncommutative spaces". In this talk, I will discuss a calculation of the topological K-theory of the dg category of graded matrix factorizations associated to a quasi-homogeneous polynomial with complex coefficients in terms of a classical topological invariant of a complex hypersurface singularity: the Milnor fiber and its monodromy.</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2017&diff=14176Algebraic Geometry Seminar Fall 20172017-09-19T18:46:05Z<p>Kjuchukova: /* Fall 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B321.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--and for [[Algebraic Geometry Seminar Spring 2017 | the next semester]].---><br />
<!-- and for [[Algebraic Geometry Seminar | this semester]].---><br />
<br />
==Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2017 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 29<br />
|[http://www.math.unibe.ch/ueber_uns/personen/prof_dr_baader_sebastian/index_ger.html// Sebastian Baader (Bern)] <br />
|[[#Sebastian Baader|TBA]]<br />
|Kjuchukova<br />
<br />
|-<br />
|October 6<br />
|[http://www.math.wisc.edu/~mkbrown5// Michael Brown (UW-Madison)] <br />
|[[#Michael Brown|Topological K-theory of equivariant singularity categories]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Michael Brown===<br />
<br />
'''Topological K-theory of equivariant singularity categories'''<br />
<br />
This is joint work with Tobias Dyckerhoff. Topological K-theory of complex-linear dg categories is a notion introduced by Blanc in his recent article "Topological K-theory of complex noncommutative spaces". In this talk, I will discuss a calculation of the topological K-theory of the dg category of graded matrix factorizations associated to a quasi-homogeneous polynomial with complex coefficients in terms of a classical topological invariant of a complex hypersurface singularity: the Milnor fiber and its monodromy.</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14149Geometry and Topology Seminar 2019-20202017-09-18T13:43:21Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|Jiyuan Han (University of Wisconsin-Madison)<br />
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]<br />
|Local <br />
|-<br />
|September 22<br />
|Sigurd Angenent (UW-Madison)<br />
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]<br />
|Local<br />
|-<br />
|September 29<br />
|Ke Zhu (Minnesota State University)<br />
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]<br />
|Bing Wang<br />
|-<br />
|October 6<br />
|Shaosai Huang (Stony Brook)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|Sebastian Baader (Bern)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"TBA"<br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14047Geometry and Topology Seminar 2019-20202017-09-04T17:46:45Z<p>Kjuchukova: /* Fall 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|TBA<br />
|TBA<br />
|TBA <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 29<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 6<br />
|Shaosai Huang(Stony Brook)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|(reserved)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu(University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13382Graduate/Postdoc Topology and Singularities Seminar2017-02-16T20:12:36Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>== 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 />
|}<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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13381Graduate/Postdoc Topology and Singularities Seminar2017-02-16T20:12:08Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>== 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"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number" Part II<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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13196Geometry and Topology Seminar 2019-20202017-01-31T19:59:18Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13195Geometry and Topology Seminar 2019-20202017-01-31T19:58:35Z<p>Kjuchukova: /* Spring Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13107Graduate/Postdoc Topology and Singularities Seminar2017-01-23T21:28:35Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>== 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 />
| <br />
| <br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number"<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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12999Geometry and Topology Seminar 2019-20202017-01-16T12:56:11Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12978Geometry and Topology Seminar 2019-20202017-01-14T09:04:09Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| Reserved<br />
| <br />
| Kjuchukova<br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12814Geometry and Topology Seminar 2019-20202016-12-09T17:37:23Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "TBA"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Gaven Marin ===<br />
''TBA''<br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12411Graduate/Postdoc Topology and Singularities Seminar2016-09-28T17:50:19Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>== 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 that 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 (M)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (M)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12280Colloquia/Fall182016-09-13T02:23:49Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|Directed paths: from Ramsey to Pseudorandomness<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|TBA<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|TBA<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|TBA<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|TBA<br />
| Feldman<br />
|<br />
|-<br />
|Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10<br />
| '''No Colloquium''' <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
=== September 16: Po-Shen Loh (CMU) ===<br />
Title: Directed paths: from Ramsey to Pseudorandomness<br />
<br />
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed<br />
paths in graphs, we discover a series of rich and surprising connections<br />
that lead into the theory around a fundamental result in Combinatorics:<br />
Szemeredi's Regularity Lemma, which roughly states that every graph (no<br />
matter how large) can be well-approximated by a bounded-complexity<br />
pseudorandom object. Using these relationships, we prove that every<br />
coloring of the edges of the transitive N-vertex tournament using three<br />
colors contains a directed path of length at least sqrt(N) e^{log^* N}<br />
which entirely avoids some color. The unusual function log^* is the<br />
inverse function of the tower function (iterated exponentiation).<br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12265Colloquia/Fall182016-09-09T23:04:35Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|TBA<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|TBA<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (UPenn)<br />
|[[# | ]]<br />
|Kjuchukova<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|TBA<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|TBA<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|TBA<br />
| Feldman<br />
|<br />
|-<br />
|Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10<br />
| '''No Colloquium''' <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12264Colloquia/Fall182016-09-09T23:04:30Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|TBA<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|TBA<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (UPenn)<br />
|[[# | ]]<br />
|Kjuchukova<br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|TBA<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|TBA<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|TBA<br />
| Feldman<br />
|<br />
|-<br />
|Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10<br />
| '''No Colloquium''' <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (UPenn)<br />
|[[# | ]]<br />
|Kjuchukova<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12263Colloquia/Fall182016-09-09T22:51:49Z<p>Kjuchukova: /* Spring 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|TBA<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)<br />
|TBA<br />
| Street<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)<br />
|Geometric Ramsey theory<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| <br />
|<br />
| <br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|TBA<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|TBA<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|TBA<br />
| Feldman<br />
|<br />
|-<br />
|Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])<br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)<br />
|Siegel's problem on small volume lattices<br />
| Marshall<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
|<br />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10<br />
| '''No Colloquium''' <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[# | ]]<br />
|Dymarz<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (UPenn)<br />
|[[# | ]]<br />
|Kjuchukova<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]<br />
|[[# | ]]<br />
|Erman<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|TBA<br />
| Maxim <br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== September 30: Akos Magyar (University of Georgia) === <br />
Title: Geometric Ramsey theory<br />
<br />
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.<br />
<br />
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===<br />
Title: Siegel's problem on small volume lattices<br />
<br />
Abstract: We outline in very general terms the history and the proof of the identification<br />
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3<br />
Coxeter group extended by the involution preserving the symmetry of this<br />
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.<br />
This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the<br />
signature formula identifying the (2,3,7)-triangle group as having minimal<br />
co-area.<br />
<br />
There are strong connections with arithmetic hyperbolic geometry in<br />
the proof, and the result has applications in the maximal symmetry groups<br />
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem<br />
and Siegel's result do.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12043Colloquia/Fall182016-08-10T20:15:08Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|September 16<br />
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)<br />
|[[# TBA | TBA ]]<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
| <br />
|[[# | ]]<br />
| <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
| Cook<br />
|<br />
|-<br />
|October 7<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|[[# TBA | TBA ]]<br />
| Maxim <br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|[[# TBA | TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| Linda Reichl (UT Austin)<br />
|[[# TBA | TBA ]]<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|[[# TBA | TBA ]]<br />
| Feldman<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 10<br />
| <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Tuesday, March 7, 4PM (Distinguished Lecture)<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|Wednesday, March 8, 2:25PM <br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[# | ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|Wednesday, March 29 (Wasow)<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# TBA| TBA]]<br />
|Tran<br />
|<br />
|-<br />
|March 31<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 14<br />
| Wilfrid Gangbo<br />
|[[# | ]]<br />
|Feldman & Tran<br />
|<br />
|-<br />
|April 21<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 28<br />
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] <br />
|[[# TBA| TBA ]]<br />
|Li<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=11950Colloquia/Fall182016-06-28T14:48:49Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Ellenberg <br />
|<br />
|-<br />
|September 16<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Maxim <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
| TBA (TBA)<br />
|[[# TBA| TBA ]] <br />
| Hung Tran<br />
|<br />
|-<br />
|October 7<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|[[# TBA | TBA ]]<br />
| Maxim <br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|[[# TBA | TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|October 28<br />
| Linda Reichl (UT Austin)<br />
|[[# TBA | TBA ]]<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)<br />
|[[# TBA | TBA ]]<br />
| Feldman<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 10<br />
| <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 10<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| [http://pages.iu.edu/~temam/ Roger Teman] (Indiana University) <br />
|[[# TBA | TBA ]]<br />
| Smith<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 14<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 21<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 28<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=11945Colloquia/Fall182016-06-20T16:11:04Z<p>Kjuchukova: /* Fall 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Ellenberg <br />
|<br />
|-<br />
|September 16<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Ellenberg<br />
|<br />
|-<br />
|September 23<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Maxim <br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
| TBA (TBA)<br />
|[[# TBA| TBA ]] <br />
| Hung Tran<br />
|<br />
|-<br />
|October 7<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|[[# TBA | TBA ]]<br />
| Maxim <br />
|<br />
|-<br />
|October 14<br />
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)<br />
|[[# TBA | TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|Tentatively Reserved <br />
|[[# | ]]<br />
|Kjuchukova <br />
|<br />
|-<br />
|October 28<br />
| Linda Reichl (UT Austin)<br />
|[[# TBA | TBA ]]<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|November 4<br />
| TBA (TBA)<br />
|[[# | ]]<br />
| Feldman<br />
|<br />
|-<br />
|November 11<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 18<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 9<br />
| Reserved for possible job talks<br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 20<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3<br />
| <br />
|[[# | ]]<br />
| <br />
|-<br />
|February 10<br />
| <br />
|[[# | ]] <br />
| <br />
|<br />
|-<br />
|February 17<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 24<br />
| <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|March 3<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 10<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|March 17<br />
| [http://pages.iu.edu/~temam/ Roger Teman] (Indiana University) <br />
|[[# TBA | TBA ]]<br />
| Smith<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 7<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 14<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 21<br />
| <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|April 28<br />
| <br />
|[[# | ]]<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=11754Colloquia/Fall182016-04-06T20:34:41Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==[[Tentative Colloquia|Tentative schedule for next semester]] ==<br />
<br />
== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
|<!--[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)--><br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!--Host--><br />
|-<br />
| '''January 28 (Th 4pm VV901)''' <br />
| [https://web.math.princeton.edu/~ssivek/ Steven Sivek] (Princeton)<br />
| [[Colloquia#September 11: Speaker (University) | The augmentation category of a Legendrian knot]] <br />
| Ellenberg<br />
|-<br />
| '''January 29''' <br />
|[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)<br />
| [[Colloquia#September 11: Ana Caraiani (Princeton) | Locally symmetric spaces, torsion classes, and the geometry of period domains]] <br />
| Ellenberg<br />
|-<br />
| '''February 5''' <br />
|[http://math.uchicago.edu/~souganidis/ Takis Souganidis] (University of Chicago)<br />
| [[Colloquia#September 11: Takis Souganidis (University of Chicago) | Scalar Conservation Laws with Rough Dependence]]<br />
| Lin<br />
|-<br />
| '''February 12''' <br />
|[http://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU) <br />
| [[Colloquia#February 12: Gautam Iyer (CMU)| Homogenization and Anomalous Diffusion]]<br />
| Jean-Luc<br />
|-<br />
| '''February 19''' <br />
| [https://people.math.osu.edu/lafont.1/ Jean-François Lafont] (Ohio State) <br />
| [[Colloquia#February 19: Jean-François Lafont (Ohio State) | Rigidity and flexibility of almost-isometries]]<br />
| Dymarz<br />
|-<br />
| '''February 26''' <br />
|Hiroyoshi Mitake (Hiroshima university) <br />
| [[Colloquia#February 26: Hiroyoshi Mitake (Hiroshima university) | On asymptotic speed of the crystal growth]]<br />
| Tran<br />
|-<br />
| '''March 4''' <br />
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)<br />
| [[Colloquia#September 11: Guillaume Bal (Columbia University) | Inverse and Control Transport Problems]]<br />
| Li, Jin<br />
|-<br />
| '''March 11''' <br />
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)<br />
| [[Colloquia#March 11: Mitchell Luskin (UMN) | Mathematical Modeling of Incommensurate 2D Materials]]<br />
| Li<br />
|-<br />
| '''March 18''' <br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan) <br />
| CANCELED<br />
| Dymarz<br />
|-<br />
| '''March 25''' <br />
| Spring Break<!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <br />
| <br />
|<br />
|-<br />
| '''April 8''' <br />
| [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton) <br />
| [[Colloquia#April 8: Alexandru Ionescu (Princeton) | On long-term existence of solutions of water wave models]] <br />
| Wainger/Seeger<br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Nodal Domains of Eigenfunctions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | Liquid crystals and their (algebraic) topology]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
=== January 28: Steven Sivek (Princeton) === <br />
Title: The augmentation category of a Legendrian knot<br />
<br />
Abstract: A well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle. One prominent example of this is Nadler and Zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the Fukaya category.<br />
<br />
The goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to Legendrian knots in the standard contact 3-space. This construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. I will describe some interesting properties of this category and relate it to a category of sheaves on the plane. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Maslow.<br />
<br />
=== January 29: Ana Caraiani (Princeton) === <br />
Title: Locally symmetric spaces, torsion classes, and the geometry of period domains<br />
<br />
Abstract: The Langlands program is an intricate network of conjectures, which are meant to connect different areas of mathematics, such as number theory, harmonic analysis and representation theory. One striking consequence of the Langlands program is the Ramanujan conjecture, which is a statement purely within harmonic analysis, about the growth rate of Fourier coefficients of modular forms. It turns out to be intimately connected to the Weil conjectures, a statement about the cohomology of projective, smooth varieties defined over finite fields.<br />
<br />
I will explain this connection and then move towards a mod p analogue of these ideas. More precisely, I will explain a strategy for understanding torsion occurring in the cohomology of locally symmetric spaces and how to detect which degrees torsion will contribute to. The main theorem is joint work with Peter Scholze and relies on a p-adic version of Hodge theory and on recent developments in p-adic geometry.<br />
<br />
<br />
=== February 5: Takis Souganidis (University of Chicago) === <br />
Title: Scalar Conservation Laws with Rough Dependence<br />
<br />
I will present a recently developed theory for scalar conservation laws with nonlinear multiplicative rough signal dependence. I will describe the difficulties, introduce the notion of pathwise entropy/kinetic solution and its well-posedness. I will also talk about the long time behavior of the solutions as well as some regularization by noise type results.<br />
<br />
=== February 12: Gautam Iyer (CMU) ===<br />
<br />
Homogenization and Anomalous Diffusion<br />
<br />
Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities.<br />
While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results<br />
motivated by fluid dynamics. One well known result in this direction is by GI Taylor estimating the dispersion rate of a solute in a pipe. The<br />
length scales involved in typical pipelines, however, are too short for this result to apply. I will conclude with a few recent "intermediate time" results describing the effective behaviour in scaling regimes outside those of standard homogenization results.<br />
<br />
=== February 19: Jean-François Lafont (Ohio State) ===<br />
<br />
Rigidity and flexibility of almost-isometries<br />
<br />
An almost isometry (AI) is a quasi-isometry (QI) with multiplicative<br />
constant =1. Given two metrics on a closed manifold, Milnor-Swarc implies<br />
that the lifted metrics on the universal cover are QI to each other. When are<br />
they AI to each other? In the rigidity direction, we give various examples<br />
where the only time such lifts are AI is when they are isometric (joint with<br />
Kar and Schmidt). In the flexible direction, we show that for higher genus<br />
surfaces, any two metrics have lifts which, after possibly scaling one of the<br />
lifted metrics, are AI to each other (joint with Schmidt and van Limbeek). In<br />
the latter examples, one can further show that the AI is usually not equivariant<br />
with respect to the group actions.<br />
<br />
=== February 26: Hiroyoshi Mitake (Hiroshima University) ===<br />
In the talk, I will propose a model equation to study the crystal growth as a prototype, which is described by a level-set mean curvature flow equation with driving and source terms. We establish the well-posedness of solutions, and study the asymptotic speed. Interestingly, a new type of nonlinear phenomena in terms of asymptotic speed of solutions appears because of the double nonlinear effects coming from the surface evolution and the source term, which is sensitive to the shapes of source terms. This is a joint work with Y. Giga (U. Tokyo), and H. V. Tran (U. Wisconsin-Madison). <br />
<br />
=== March 11: Mitchell Luskin (UMN) ===<br />
Title: Mathematical Modeling of Incommensurate 2D Materials<br />
<br />
Abstract: Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation.<br />
<br />
Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.<br />
<br />
===March 18: Ralf Spatzier (UMichigan)===<br />
<br />
CANCELED: Rigidity in Geometry and Dynamics<br />
<br />
I will survey some rigidity phenomena in dynamics and also geometry, with emphasis on the notion of higher rank.<br />
This first emerged in Margulis’ celebrated work on superrrigidity but has also been important in more recent work on symmetry in dynamical systems.<br />
How special is it for maps commute with each other? Smale asked this problem fifty years ago, and answers are finally emerging. Much depends on the differentiability<br />
of the maps: it gets harder the more differentiable the map is. Sometimes we can even classify such maps. I’ll discuss this and<br />
related phenomena.<br />
<br />
<br />
<br />
=== April 8: Alexandru Ionescu (Princeton) ===<br />
<br />
Title: On long-term existence of solutions of water wave models<br />
<br />
I will talk about some recent work on long-term/global regularity of solutions of water wave models in 2 and 3 dimensions. The <br />
models we consider describe the evolution of an inviscid perfect fluid in<br />
a free boundary domain, under the influence of gravity and/or surface<br />
tension. This is joint work with Fabio Pusateri and, in part, with Yu Deng and<br />
Benoit Pausader.<br />
<br />
<br />
=== April 29: Randall Kamien (U Penn) ===<br />
<br />
Title: Liquid Crystals and their (Algebraic) Topology<br />
<br />
Liquid Crystals, the materials in your iPhone, are complex materials with varying degrees of internal order. I will discuss and demonstrate how algebraic topology can be used to identify and characterize long-lived configurations. I will also describe how conic sections naturally arise in these structures as intersections of simple polynomials.<br />
<br />
===<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=11594Geometry and Topology Seminar 2019-20202016-03-04T18:02:11Z<p>Kjuchukova: /* Spring Abstracts */</p>
<hr />
<div>Traditionally, the [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> In Spring of 2016, the seminar will meet on '''Thursdays''' at 2:25PM in B 231 of Van Vleck. <br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in B 231 of Van Vleck. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
|<br />
|<br />
| <br />
|-<br />
|February 11<br />
| [http://www.math.wisc.edu/~wang Botong Wang] (UW Madison)<br />
| [[#Botong Wang|''A family of Symplectic-Complex Calabi-Yau Manifolds that are NonKahler'']]<br />
| (local)<br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| [https://www.math.purdue.edu/~psolapur/ Partha Solapurkar] (Purdue University)<br />
| [[#Partha Solapurkar|''Some new surfaces of general type with maximal Picard number'']]<br />
| [http://www.math.wisc.edu/~wang Botong Wang]<br />
|-<br />
|March 3<br />
| [https://math.la.asu.edu/~kotschwar/ Brett Kotschwar] (Arizona State University)<br />
| [[#Brett Kotschwar|''Ricci flow and bounded curvature'']]<br />
| [https://sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|Friday March 4 (1:20-2:10pm in VV B211)<br />
| [http://homepages.math.uic.edu/~cantrell/ Mike Cantrell] (UIC)<br />
| [[#Mike Cantrell|'"Asymptotic shapes for ergodic families of metrics on nilpotent groups"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Wednesday March 9 (1:20-2:10pm in VV B211)<br />
| [http://www.uncg.edu/~t_fernos/ Talia Fernos] (Greensboro)<br />
| [[#Talia Fernos|''The Roller Compactification and CAT(0) Cube Complexes'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''Knots Transverse to a Vector Field'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
|<br />
|<br />
|<br />
|-<br />
|Friday March 18 (1:20-2:10pm in VV B211)<br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (UMichigan)<br />
| [[#Ralf Spatzier|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| [https://people.math.osu.edu/kennedy.28/ Gary Kennedy] (Ohio State University)<br />
| TBA<br />
| Gonzalez Villa<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
===Brett Kotschwar===<br />
<br />
''Ricci flow and bounded curvature''<br />
<br />
The problem of determining when a given solution to the Ricci flow with initially bounded curvature will continue to have bounded curvature has bearing on both the uniqueness and long-time existence of solutions to the flow. I will discuss two results in this direction which are equally valid in the noncompact setting, the first based on a simple proof of an extension to the standard uniqueness theorem of Hamilton and Chen-Zhu, and the second, joint with Ovidiu Munteanu and Jiaping Wang, based on new explicit local estimates of the curvature under a uniform bound on the Ricci tensor.<br />
<br />
===Partha Solapurkar===<br />
<br />
''Some new surfaces of general type with maximal Picard number''<br />
<br />
The Picard number $ \rho(X) $ of a surface $ X $ is the rank of its Neron-Severi group. It is bounded above by the Hodge number $ h^{11}(X) $. We say that a surface has maximal Picard number if it has the largest possible Picard number: $ \rho(X) = h^{11}(X) $. In 1972, Shioda constructed elliptic modular surfaces and among other things, proved that they have maximal Picard number. Our first idea is to take elliptic modular surfaces and replace each elliptic curve with a canonically constructed genus 2 curve. Under nice circumstances the resulting surfaces do indeed have maximal Picard number. There is also a second set of examples that arise as the total space of the moduli space of quaternionic Shimura curves. This is joint work with my advisor Prof. D. Arapura. <br />
<br />
===Botong Wang===<br />
<br />
''A family of Symplectic-Complex Calabi-Yau Manifolds that are NonKahler''<br />
<br />
A Kahler manifold is a smooth manifold with compatible complex and symplectic structures. In general, a compact manifold which admits both complex and symplectic structures may not admit any Kahler structure. Hodge theory and hard Lefschetz theorem have very strong implications on the homotopy type of compact Kahler manifolds. We introduce a family of 6-dimensional compact manifolds $M(A)$, which admit both Calabi-Yau symplectic and Calabi-Yau complex structures. They satisfy all the consequences of classical Hodge theory and hard Lefschetz theorem. However, we show that they are not homotopy equivalent to any compact Kahler manifold using a recently developed cohomology jump loci method. This is joint work with Lizhen Qin.<br />
<br />
===Mike Cantrell===<br />
<br />
"Asymptotic shapes for ergodic families of metrics on nilpotent groups"<br />
<br />
Let G be a finitely generated virtually nilpotent group. We consider three closely related problems: (i) convergence to a deterministic asymptotic cone for an equivariant ergodic family of inner metrics on G, generalizing Pansu’s theorem; (ii) the asymptotic shape theorem for First Passage Percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of G; (iii) the sub-additive ergodic theorem over a general ergodic G-action. The<br />
limiting objects are given in terms of a Carnot-Carathérodory metric on the graded nilpotent group associated to the Mal’cev completion of G.<br />
<br />
===Talia Fernos===<br />
<br />
"The Roller Compactification and CAT(0) Cube Complexes"<br />
<br />
The Roller compactification is a beautiful object that ties together the combinatorial and geometric properties that characterize CAT(0) cube complexes. In this talk, we will discuss this compactification in the context of superrigidity, the fixed point Property (FC), and the abundance of regular elements (i.e. automorphisms that are rank-1 in each irreducible factor). These results are collaborations with Caprace, Chatterji, and Iozzi, as well as, Lécureux, and Mathéus.<br />
<br />
<br />
<br />
===Patricia Cahn===<br />
<br />
"Knots Transverse to a Vector Field"<br />
<br />
We study knots transverse to a fixed vector field V on a 3-manifold M up to the corresponding isotopy relation. Such knots are equipped with a natural framing. Motivated by questions in contact topology, it is natural to ask whether two V-transverse knots which are isotopic as framed knots and homotopic through V-transverse immersed curves must be isotopic through V-transverse knots. When M is R^3 and V is the vertical vector field the answer is yes. However, we construct examples which show the answer to this question can be no in other 3-manifolds, specifically S^1-fibrations over surfaces of genus at least 2. We also give a general classification of knots transverse to a vector field in an arbitrary closed oriented 3-manifold M. We show this classification is particularly simple when V is the co-orienting vector field of a tight contact structure, or when M is irreducible and atoroidal. Lastly, we apply our results to study loose Legendrian knots in overtwisted contact manifolds, and generalize results of Dymara and Ding-Geiges. This work is joint with Vladimir Chernov.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=11593Geometry and Topology Seminar 2019-20202016-03-04T17:59:38Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>Traditionally, the [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> In Spring of 2016, the seminar will meet on '''Thursdays''' at 2:25PM in B 231 of Van Vleck. <br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in B 231 of Van Vleck. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
|<br />
|<br />
| <br />
|-<br />
|February 11<br />
| [http://www.math.wisc.edu/~wang Botong Wang] (UW Madison)<br />
| [[#Botong Wang|''A family of Symplectic-Complex Calabi-Yau Manifolds that are NonKahler'']]<br />
| (local)<br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| [https://www.math.purdue.edu/~psolapur/ Partha Solapurkar] (Purdue University)<br />
| [[#Partha Solapurkar|''Some new surfaces of general type with maximal Picard number'']]<br />
| [http://www.math.wisc.edu/~wang Botong Wang]<br />
|-<br />
|March 3<br />
| [https://math.la.asu.edu/~kotschwar/ Brett Kotschwar] (Arizona State University)<br />
| [[#Brett Kotschwar|''Ricci flow and bounded curvature'']]<br />
| [https://sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|Friday March 4 (1:20-2:10pm in VV B211)<br />
| [http://homepages.math.uic.edu/~cantrell/ Mike Cantrell] (UIC)<br />
| [[#Mike Cantrell|'"Asymptotic shapes for ergodic families of metrics on nilpotent groups"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Wednesday March 9 (1:20-2:10pm in VV B211)<br />
| [http://www.uncg.edu/~t_fernos/ Talia Fernos] (Greensboro)<br />
| [[#Talia Fernos|''The Roller Compactification and CAT(0) Cube Complexes'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''Knots Transverse to a Vector Field'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
|<br />
|<br />
|<br />
|-<br />
|Friday March 18 (1:20-2:10pm in VV B211)<br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (UMichigan)<br />
| [[#Ralf Spatzier|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| [https://people.math.osu.edu/kennedy.28/ Gary Kennedy] (Ohio State University)<br />
| TBA<br />
| Gonzalez Villa<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
===Brett Kotschwar===<br />
<br />
''Ricci flow and bounded curvature''<br />
<br />
The problem of determining when a given solution to the Ricci flow with initially bounded curvature will continue to have bounded curvature has bearing on both the uniqueness and long-time existence of solutions to the flow. I will discuss two results in this direction which are equally valid in the noncompact setting, the first based on a simple proof of an extension to the standard uniqueness theorem of Hamilton and Chen-Zhu, and the second, joint with Ovidiu Munteanu and Jiaping Wang, based on new explicit local estimates of the curvature under a uniform bound on the Ricci tensor.<br />
<br />
===Partha Solapurkar===<br />
<br />
''Some new surfaces of general type with maximal Picard number''<br />
<br />
The Picard number $ \rho(X) $ of a surface $ X $ is the rank of its Neron-Severi group. It is bounded above by the Hodge number $ h^{11}(X) $. We say that a surface has maximal Picard number if it has the largest possible Picard number: $ \rho(X) = h^{11}(X) $. In 1972, Shioda constructed elliptic modular surfaces and among other things, proved that they have maximal Picard number. Our first idea is to take elliptic modular surfaces and replace each elliptic curve with a canonically constructed genus 2 curve. Under nice circumstances the resulting surfaces do indeed have maximal Picard number. There is also a second set of examples that arise as the total space of the moduli space of quaternionic Shimura curves. This is joint work with my advisor Prof. D. Arapura. <br />
<br />
===Botong Wang===<br />
<br />
''A family of Symplectic-Complex Calabi-Yau Manifolds that are NonKahler''<br />
<br />
A Kahler manifold is a smooth manifold with compatible complex and symplectic structures. In general, a compact manifold which admits both complex and symplectic structures may not admit any Kahler structure. Hodge theory and hard Lefschetz theorem have very strong implications on the homotopy type of compact Kahler manifolds. We introduce a family of 6-dimensional compact manifolds $M(A)$, which admit both Calabi-Yau symplectic and Calabi-Yau complex structures. They satisfy all the consequences of classical Hodge theory and hard Lefschetz theorem. However, we show that they are not homotopy equivalent to any compact Kahler manifold using a recently developed cohomology jump loci method. This is joint work with Lizhen Qin.<br />
<br />
===Mike Cantrell===<br />
<br />
"Asymptotic shapes for ergodic families of metrics on nilpotent groups"<br />
<br />
Let G be a finitely generated virtually nilpotent group. We consider three closely related problems: (i) convergence to a deterministic asymptotic cone for an equivariant ergodic family of inner metrics on G, generalizing Pansu’s theorem; (ii) the asymptotic shape theorem for First Passage Percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of G; (iii) the sub-additive ergodic theorem over a general ergodic G-action. The<br />
limiting objects are given in terms of a Carnot-Carathérodory metric on the graded nilpotent group associated to the Mal’cev completion of G.<br />
<br />
===Talia Fernos===<br />
<br />
"The Roller Compactification and CAT(0) Cube Complexes"<br />
<br />
The Roller compactification is a beautiful object that ties together the combinatorial and geometric properties that characterize CAT(0) cube complexes. In this talk, we will discuss this compactification in the context of superrigidity, the fixed point Property (FC), and the abundance of regular elements (i.e. automorphisms that are rank-1 in each irreducible factor). These results are collaborations with Caprace, Chatterji, and Iozzi, as well as, Lécureux, and Mathéus.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=11353Geometry and Topology Seminar 2019-20202016-01-28T05:39:54Z<p>Kjuchukova: </p>
<hr />
<div>Traditionally, the [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> In Spring of 2016, the seminar will meet on '''Thursdays''' at 2:25PM in B 231 of Van Vleck. <br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in B 231 of Van Vleck. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [https://math.la.asu.edu/~kotschwar/ Brett Kotschwar] (Arizona State University)<br />
| [[#Brett Kotschwar|''TBA'']]<br />
| [https://sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|Friday March 4 (1:20-2:10pm in VV B211)<br />
| [http://homepages.math.uic.edu/~cantrell/ Mike Cantrell] (UIC)<br />
| [[#Mike Cantrell|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Wednesday March 9 (1:20-2:10pm in VV B211)<br />
| [http://www.uncg.edu/~t_fernos/ Talia Fernos] (Greensboro)<br />
| [[#Talia Fernos|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
|<br />
|<br />
|<br />
|-<br />
|Friday March 18 (1:20-2:10pm in VV B211)<br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (UMichigan)<br />
| [[#Ralf Spatzier|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| GK (TBC)<br />
| TBA<br />
| Gonzalez Villa<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=11352Geometry and Topology Seminar 2019-20202016-01-28T05:39:15Z<p>Kjuchukova: </p>
<hr />
<div>Traditionally, the [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br> In Spring of 2016, the seminar will meet on '''Thursdays''' at 2:25PM in B 231 of Van Vleck<br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in B 231 of Van Vleck. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [https://math.la.asu.edu/~kotschwar/ Brett Kotschwar] (Arizona State University)<br />
| [[#Brett Kotschwar|''TBA'']]<br />
| [https://sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|Friday March 4 (1:20-2:10pm in VV B211)<br />
| [http://homepages.math.uic.edu/~cantrell/ Mike Cantrell] (UIC)<br />
| [[#Mike Cantrell|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Wednesday March 9 (1:20-2:10pm in VV B211)<br />
| [http://www.uncg.edu/~t_fernos/ Talia Fernos] (Greensboro)<br />
| [[#Talia Fernos|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
|<br />
|<br />
|<br />
|-<br />
|Friday March 18 (1:20-2:10pm in VV B211)<br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (UMichigan)<br />
| [[#Ralf Spatzier|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| GK (TBC)<br />
| TBA<br />
| Gonzalez Villa<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=11351Geometry and Topology Seminar 2019-20202016-01-28T05:38:29Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in B 231 of Van Vleck. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [https://math.la.asu.edu/~kotschwar/ Brett Kotschwar] (Arizona State University)<br />
| [[#Brett Kotschwar|''TBA'']]<br />
| [https://sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|Friday March 4 (1:20-2:10pm in VV B211)<br />
| [http://homepages.math.uic.edu/~cantrell/ Mike Cantrell] (UIC)<br />
| [[#Mike Cantrell|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Wednesday March 9 (1:20-2:10pm in VV B211)<br />
| [http://www.uncg.edu/~t_fernos/ Talia Fernos] (Greensboro)<br />
| [[#Talia Fernos|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
|<br />
|<br />
|<br />
|-<br />
|Friday March 18 (1:20-2:10pm in VV B211)<br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (UMichigan)<br />
| [[#Ralf Spatzier|''TBA'']]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| GK (TBC)<br />
| TBA<br />
| Gonzalez Villa<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=11231Geometry and Topology Seminar Spring 20162016-01-26T17:08:23Z<p>Kjuchukova: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room B231 of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in VV B231. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=11230Geometry and Topology Seminar Spring 20162016-01-26T17:04:32Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room B231 of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in VV B231. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=11223Geometry and Topology Seminar Spring 20162016-01-26T14:51:05Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room B231 of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM in VV B231. <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=11222Geometry and Topology Seminar Spring 20162016-01-26T14:50:25Z<p>Kjuchukova: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room B231 of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10899Geometry and Topology Seminar 2019-20202015-12-22T22:48:40Z<p>Kjuchukova: /* Ryan Blair */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
''Distance and Exceptional Surgeries on Knots''<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10898Geometry and Topology Seminar 2019-20202015-12-22T22:47:05Z<p>Kjuchukova: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
===Ryan Blair===<br />
<br />
"Distance and Exceptional Surgeries on Knots"<br />
<br />
Distance is a measure of complexity for a bicompressible surface in a 3-manifold which is defined using the curve complex for the surface. Recently, distance has been used to better understand Dehn surgery on knots in 3-manifolds. In particular, I will present results which show that knots with high distance surfaces do not admit non-hyperbolic surgeries or cosmetic surgeries. Applications to the cabling conjecture and the Berge conjecture will also be discussed.<br />
<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10897Geometry and Topology Seminar 2019-20202015-12-22T22:42:45Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
<br />
<!-- Spring 2016: [[Geometry_and_Topology_Seminar_Spring_2016]]<br />
<br><br> --><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''Distance and Exceptional Surgeries on Knots'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| [http://personal.bgsu.edu/~xiex/ Xiangdong Xie] (Bowling Green University)<br />
| [[#Xiangdong Xie|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.mcgill.ca/node/7171 Jingyin Huang] (McGill University)<br />
| [[#Jingyin Huang|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''Stability for the multidimensional rigid body and singular curves'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich|''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong|''Milnor Fiber of Complex Hyperplane Arrangement'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''Stability for the multidimensional rigid body and singular curves''<br />
<br />
A classical result of Euler says that the rotation of a<br />
torque-free 3-dimensional rigid body about the short or the long axis is<br />
stable, while the rotation about the middle axis is unstable. I will<br />
present a multidimensional generalization of this result and explain how<br />
it can be proved using some basic algebraic geometry of singular curves.<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
===Quinton Westerich===<br />
<br />
''Harmonic Chern Forms on Polarized Kähler Manifolds''<br />
<br />
Abstract: The higher K-energies are functionals whose critical points <br />
give Kähler metrics with harmonic Chern forms. In this talk, we relate <br />
the higher K-energies to discriminants and use the theory of stable <br />
pairs to obtain results on their boundedness and asymptotics.<br />
<br />
<br />
===Tommy Wong===<br />
<br />
''Milnor Fiber of Complex Hyperplane Arrangement''<br />
<br />
The existence of Milnor fibration creates rooms and provides a platform to discuss the topology of complex algebraic varieties. In this talk, the study of hyperplane arrangements will be specified. <br />
Many open questions have been raised subject to the Milnor fiber of the mentioned fibration. For instance,while the homology of the arrangement complement can be described by the Orlik-Soloman Algebra, which is combinatorically determined by the intersection poset, it has been conjectured that the poset also determines the homology of the Milnor fiber.<br />
There are active work on this open conjecture, especially in C^3. Several classical results will be mentioned in the talk. A joint work with Su, serving as an improvement of some of the classical work, will also be briefly described.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=10814Geometry and Topology Seminar Spring 20162015-12-01T19:52:34Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room TBA of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| [https://guests.mpim-bonn.mpg.de/pcahn/ Patricia Cahn] (Max Planck)<br />
| [[#Patricia Cahn|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=10671Geometry and Topology Seminar Spring 20162015-11-12T16:29:51Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room TBA of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (CSULB)<br />
| [[#Ryan Blair|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_Spring_2016&diff=10670Geometry and Topology Seminar Spring 20162015-11-12T16:28:49Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room TBA of Van Vleck Hall on THURSDAY from 2:25pm - 3:15pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<!-- == Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
--><br />
<br />
== Spring 2016 ==<br />
<br />
In Spring of 2016, the seminar will meet on Thursdays at 2:25PM (location TBA). <br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 21<br />
| <br />
| <br />
| <br />
|-<br />
|January 28<br />
| [http://web.csulb.edu/~rblair/ Ryan Blair] (UCSLB)<br />
| [[#Ryan Blair|''TBA'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|-<br />
|February 4<br />
| <br />
| <br />
| <br />
|-<br />
|February 11<br />
| <br />
| <br />
| <br />
|-<br />
|February 18<br />
| <br />
| <br />
| <br />
|-<br />
|February 25<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| <br />
| <br />
| <br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24 <br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| <br />
| <br />
| <br />
|-<br />
|May 5<br />
| <br />
| <br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''Classification of gravitational instantons '']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Gao Chen===<br />
''Classification of gravitational instantons''<br />
<br />
A gravitational instanton is a noncompact complete hyperkahler manifold of real dimension 4 with faster than quadratic curvature decay. In this talk, I will discuss the recent work towards the classification of gravitational instantons. This is a joint work with X. X. Chen.<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring_2016&diff=10565Colloquia/Spring 20162015-10-27T21:56:22Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
|<!-- [webpage Speaker name] (University)--><br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!--Host--><br />
|-<br />
| '''January 29''' <br />
| Amir Mohammadi (Texas-Austin) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Marshall<br />
|-<br />
| '''February 5''' <br />
|Takis Souganidis (University of Chicago)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Lin<br />
|-<br />
| '''February 12''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 19''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 26''' <br />
|Hiroyoshi Mitake (Hiroshima university) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Tran<br />
|-<br />
| '''March 4''' <br />
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Li, Jin<br />
|-<br />
| '''March 11''' <br />
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Li<br />
|-<br />
| '''March 18''' <br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan) <br />
| [[Colloquia#March 18: Ralf Spatzier (University of Michigan) | TBA]]<br />
| Dymarz<br />
|-<br />
| '''March 25''' <br />
| Spring Break<!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 8''' <br />
| Reserved <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Nodal Domains of Eigenfunctions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (University of Pennsylvania) <br />
| [[Colloquia#September 11: Julius Shaneson (University of Pennsylvania) | TBA]] <br />
| Maxim/Kjuchukova<br />
|}</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring_2016&diff=10562Colloquia/Spring 20162015-10-27T16:38:54Z<p>Kjuchukova: /* Spring 2016 */</p>
<hr />
<div>== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
|<!-- [webpage Speaker name] (University)--><br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!--Host--><br />
|-<br />
| '''January 29''' <br />
| Amir Mohammadi (Texas-Austin) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Marshall<br />
|-<br />
| '''February 5''' <br />
|Takis Souganidis (University of Chicago)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Lin<br />
|-<br />
| '''February 12''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 19''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 26''' <br />
|Hiroyoshi Mitake (Hiroshima university) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Tran<br />
|-<br />
| '''March 4''' <br />
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Li, Jin<br />
|-<br />
| '''March 11''' <br />
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Li<br />
|-<br />
| '''March 18''' <br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan) <br />
| [[Colloquia#March 18: Ralf Spatzier (University of Michigan) | TBA]]<br />
| Dymarz<br />
|-<br />
| '''March 25''' <br />
| Spring Break<!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (University of Pennsylvania) <br />
| [[Colloquia#September 11: Julius Shaneson (University of Pennsylvania) | TBA]] <br />
| Maxim/Kjuchukova<br />
|-<br />
| '''April 8''' <br />
| Reserved <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Nodal Domains of Eigenfunctions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| Reserved <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|}</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=10535Graduate/Postdoc Topology and Singularities Seminar2015-10-22T18:42:43Z<p>Kjuchukova: </p>
<hr />
<div>The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
If you would like to present a topic, please contact Tommy Wong. The seminar meets on '''Thursdays at 4pm''' (note the recent change of time) in B139VV.<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 />
|TBA<br />
|TBA<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|TBA<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|TBA<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 and Nov 5: 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 />
== 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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=10534Graduate/Postdoc Topology and Singularities Seminar2015-10-22T18:42:04Z<p>Kjuchukova: </p>
<hr />
<div>The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
If you would like to present a topic, please contact Tommy Wong. The seminar meets on \textbf{Thursdays at 4pm} (note the recent change of time) in B139VV.<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 />
|TBA<br />
|TBA<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|TBA<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|TBA<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 and Nov 5: 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 />
== 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>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=File:Hawk.jpg&diff=10486File:Hawk.jpg2015-10-19T04:31:31Z<p>Kjuchukova: </p>
<hr />
<div>Poincaré drops by the Geometry and Topology Seminar.</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10481Geometry and Topology Seminar 2019-20202015-10-18T14:44:02Z<p>Kjuchukova: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''TBA'']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Dan Cristofaro-Gardiner===<br />
''Higher-dimensional symplectic embeddings and the Fibonacci staircase''<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10480Geometry and Topology Seminar 2019-20202015-10-18T14:42:58Z<p>Kjuchukova: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''TBA'']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Dan Cristofaro-Gardiner===<br />
"Higher-dimensional symplectic embeddings and the Fibonacci staircase"<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukovahttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=10479Geometry and Topology Seminar 2019-20202015-10-18T14:42:25Z<p>Kjuchukova: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.<br />
<br><br />
For more information, contact [http://www.math.wisc.edu/~dymarz Tullia Dymarz] or [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova].<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Summer 2015 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<b>June 23 at 2pm in Van Vleck 901</b><br />
| [http://www2.warwick.ac.uk/fac/sci/maths/people/staff/david_epstein/ David Epstein] (Warwick)<br />
| [[#David Epstein (Warwick) |''Splines and manifolds.'']]<br />
| Hirsch<br />
|-<br />
|}<br />
<br />
== Summer Abstracts ==<br />
<br />
===David Epstein (Warwick)===<br />
''Splines and manifolds.''<br />
<br />
[http://www.math.wisc.edu/~rkent/Abstract.Epstein.2015.pdf Abstract (pdf)]<br />
<br />
<br />
<br />
== Fall 2015==<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 4<br />
| <br />
| <br />
| <br />
|-<br />
|September 11<br />
| [https://uwm.edu/math/people/tran-hung-1/ Hung Tran] (UW Milwaukee)<br />
| [[#Hung Tran|''Relative divergence, subgroup distortion, and geodesic divergence'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|September 18<br />
| [http://www.math.wisc.edu/~dymarz Tullia Dymarz] (UW Madison)<br />
| [[#Tullia Dymarz|''Non-rectifiable Delone sets in amenable groups'']]<br />
| (local)<br />
|-<br />
|September 25<br />
| [https://jpwolfson.wordpress.com/ Jesse Wolfson] (Uchicago)<br />
| [[#Jesse Wolfson|''Counting Problems and Homological Stability'']]<br />
| [http://www.math.wisc.edu/~mmwood/ M. Matchett Wood]<br />
|-<br />
|October 2<br />
| [https://riemann.unizar.es/~jicogo/ Jose Ignacio Cogolludo Agustín] (University of Zaragoza, Spain)<br />
| [[#Jose Ignacio Cogolludo Agustín|''Topology of curve complements and combinatorial aspects'']]<br />
|[http://www.math.wisc.edu/~maxim L. Maxim]<br />
|-<br />
|October 9<br />
| [http://people.brandeis.edu/~mcordes/ Matthew Cordes] (Brandeis)<br />
| [[#Matthew Cordes|''Morse boundaries of geodesic metric spaces'']]<br />
| [http://www.math.wisc.edu/~dymarz T. Dymarz]<br />
|-<br />
|October 16<br />
| [http://www.math.jhu.edu/~bernstein/ Jacob Bernstein] (Johns Hopkins University)<br />
| [[#Jacob Bernstein (Johns Hopkins University)|''Hypersurfaces of low entropy'']]<br />
| [http://www.sites.google.com/a/wisc.edu/lu-wang/ L. Wang]<br />
|-<br />
|October 23<br />
| [https://sites.google.com/a/wisc.edu/ysu/ Yun Su] (UW Madison)<br />
| [[#Yun Su (Brandeis)|''Higher-order degrees of hypersurface complements.'']]<br />
| (local)<br />
|-<br />
|October 30<br />
| [http://www.math.stonybrook.edu/phd-student-directory Gao Chen] (Stony Brook University)<br />
| [[#Gao Chen(Stony Brook University)|''TBA'']]<br />
| [http://www.math.wisc.edu/~bwang B.Wang]<br />
|-<br />
|November 6<br />
| [http://scholar.harvard.edu/gardiner Dan Cristofaro-Gardiner] (Harvard)<br />
| [[#Dan Cristofaro-Gardiner|''Higher-dimensional symplectic embeddings and the Fibonacci staircase'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 13<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| [[#Danny Ruberman|''Configurations of embedded spheres'']]<br />
| [http://www.math.wisc.edu/~kjuchukova Kjuchukova]<br />
|<br />
|-<br />
|November 20<br />
| [https://www.math.toronto.edu/cms/izosimov-anton/ Anton Izosimov] (University of Toronto)<br />
| [[#Anton Izosimov (University of Toronto)|''TBA'']]<br />
| [http://www.math.wisc.edu/~maribeff/ Mari-Beffa]<br />
|-<br />
|Thanksgiving Recess<br />
| <br />
|<br />
|<br />
|-<br />
|December 4<br />
| [http://www.math.wisc.edu/~westrich/ Quinton Westrich] (UW Madison)<br />
| [[#Quinton Westrich (UW Madison) |''Harmonic Chern Forms on Polarized Kähler Manifolds'']]<br />
| (local)<br />
|-<br />
|December 11<br />
|[http://kaihowong.weebly.com/ Tommy Wong] (UW Madison)<br />
| [[#Tommy Wong (UW Madison)|''Milnor Fiber of Complex Hyperplane Arrangement.'']]<br />
| (local)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
===Hung Tran===<br />
''Relative divergence, subgroup distortion, and geodesic divergence''<br />
<br />
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion<br />
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.<br />
<br />
<br />
===Tullia Dymarz===<br />
''Non-rectifiable Delone sets in amenable groups''<br />
<br />
In 1998 Burago-Kleiner and McMullen constructed the first<br />
examples of coarsely dense and uniformly discrete subsets of R^n that are<br />
not biLipschitz equivalent to the standard lattice Z^n. Similarly we<br />
find subsets inside the three dimensional solvable Lie group SOL that are<br />
not bilipschitz to any lattice in SOL. The techniques involve combining<br />
ideas from Burago-Kleiner with quasi-isometric rigidity results from<br />
geometric group theory.<br />
<br />
===Jesse Wolfson===<br />
''Counting Problems and Homological Stability''<br />
<br />
In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds. <br />
<br />
<br />
===Matthew Cordes===<br />
''Morse boundaries of geodesic metric spaces''<br />
<br />
I will introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with equivalence classes of geodesic rays that identify the ``hyperbolic directions" in that space. (A ray is Morse if quasi-geodesics with endpoints on the ray stay bounded distance from the ray.) This boundary is a quasi-isometry invariant and a visibility space. In the case of a proper CAT(0) space the Morse boundary generalizes the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. Time permitting I will also discuss some results on Morse boundary of the mapping class group and briefly describe joint work with David Hume developing a capacity dimension for the Morse boundary.<br />
<br />
===Anton Izosimov===<br />
''TBA''<br />
<br />
===Jacob Bernstein===<br />
''Hypersurfaces of low entropy''<br />
<br />
The entropy is a quantity introduced by Colding and Minicozzi and may be thought of as a rough measure of the geometric complexity of a hypersurface of Euclidean space. It is closely related to the mean curvature flow. On the one hand, the entropy controls the dynamics of the flow. On the other hand, the mean curvature flow may be used to study the entropy. In this talk I will survey some recent results with Lu Wang that show that hypersurfaces of low entropy really are simple.<br />
<br />
===Yun Su===<br />
''Higher-order degrees of hypersurface complements.''<br />
<br />
===Daniel Cristofaro-Gardiner===<br />
"Higher-dimensional symplectic embeddings and the Fibonacci staircase"<br />
<br />
McDuff and Schlenk determined when a four dimensional symplectic ellipsoid can be embedded into a ball, and found that when the ellipsoid is close to round, the answer is given by an infinite staircase determined by the odd-index Fibonacci numbers. I will explain joint work with Richard Hind, showing that a generalization of this holds in all even dimensions.<br />
<br />
===Danny Ruberman===<br />
''Configurations of embedded spheres''<br />
<br />
Configurations of lines in the plane have been studied since antiquity. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects ("lines") and other objects ("points") can be realized by actual points and lines in a projective plane over a field. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. I will explain some joint work with Laura Starkston (Stanford) giving new topological restrictions on the realization of configurations of spheres in the complex projective plane.<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kjuchukova