https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Maxim&feedformat=atomUW-Math Wiki - User contributions [en]2020-01-20T08:18:32ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=18484Geometry and Topology2019-11-24T00:15:27Z<p>Maxim: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[https://www.math.wisc.edu/~gchen/ Gao Chen] (Stony Brook 2017) <br />
Complex geometry, quaternionic geometry and octonionic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
Shaosai Huang (Stony Brook 2018)<br />
Ricci flows<br />
<br />
[https://brainhelper.wordpress.com/ Brian Hepler] (Northeastern U 2019)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing19.html Singularities in the Midwest, VI]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest, V]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=18483Geometry and Topology2019-11-24T00:15:02Z<p>Maxim: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[https://www.math.wisc.edu/~gchen/ Gao Chen] (Stony Brook 2017) <br />
Complex geometry, quaternionic geometry and octonionic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[ Shaosai Huang] (Stony Brook 2018)<br />
Ricci flows<br />
<br />
[https://brainhelper.wordpress.com/ Brian Hepler] (Northeastern U 2019)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing19.html Singularities in the Midwest, VI]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest, V]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=18482Geometry and Topology2019-11-24T00:12:08Z<p>Maxim: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[https://www.math.wisc.edu/~gchen/ Gao Chen] (Stony Brook 2017) <br />
Complex geometry, quaternionic geometry and octonionic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[https://brainhelper.wordpress.com/ Brian Hepler] (Northeastern U 2019)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing19.html Singularities in the Midwest, VI]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest, V]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=14618Geometry and Topology Seminar2017-11-29T20:48:46Z<p>Maxim: /* Brian Hepler */</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 />
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|[[#Marco Mendez-Guaraco| "Some geometric aspects of the Allen-Cahn equation"]]<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 />
|[[#Ovidiu Munteanu| "The geometry of four dimensional shrinking Ricci solitons"]]<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 />
|[[#Brian Hepler| "Deformation Formulas for Parameterizable Hypersurfaces"]]<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 />
"Hausdorff stability of round spheres under small-entropy perturbation"<br />
<br />
Colding-Minicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"Some geometric aspects of the Allen-Cahn equation"<br />
<br />
In this talk I will discuss both local and global properties of the stationary Allen-Cahn equation in closed manifolds. This equation from the theory of phase transitions has a strong connection with the theory of minimal hypersurfaces. I will summarize recent results regarding this analogy including a new min-max proof of the celebrated Almgren-Pitts theorem.<br />
<br />
=== Ovidiu Munteanu ===<br />
"The geometry of four dimensional shrinking Ricci solitons"<br />
<br />
I will present several results, joint with Jiaping Wang, about the asymptotic structure of four dimensional gradient shrinking Ricci solitons. <br />
<br />
=== Brian Hepler ===<br />
"Deformation Formulas for Parameterizable Hypersurfaces"<br />
<br />
We investigate one-parameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the Lê numbers of the special fiber in terms of the Lê numbers of the generic fiber and the characteristic polar multiplicities of the multiple-point complex, a perverse sheaf naturally associated to any parameterized hypersurface.<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=14617Geometry and Topology Seminar2017-11-29T20:48:01Z<p>Maxim: /* 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 />
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|[[#Marco Mendez-Guaraco| "Some geometric aspects of the Allen-Cahn equation"]]<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 />
|[[#Ovidiu Munteanu| "The geometry of four dimensional shrinking Ricci solitons"]]<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 />
|[[#Brian Hepler| "Deformation Formulas for Parameterizable Hypersurfaces"]]<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 />
"Hausdorff stability of round spheres under small-entropy perturbation"<br />
<br />
Colding-Minicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"Some geometric aspects of the Allen-Cahn equation"<br />
<br />
In this talk I will discuss both local and global properties of the stationary Allen-Cahn equation in closed manifolds. This equation from the theory of phase transitions has a strong connection with the theory of minimal hypersurfaces. I will summarize recent results regarding this analogy including a new min-max proof of the celebrated Almgren-Pitts theorem.<br />
<br />
=== Ovidiu Munteanu ===<br />
"The geometry of four dimensional shrinking Ricci solitons"<br />
<br />
I will present several results, joint with Jiaping Wang, about the asymptotic structure of four dimensional gradient shrinking Ricci solitons. <br />
<br />
=== Brian Hepler ===<br />
"Perverse Results on Parameterized Hypersurfaces"<br />
<br />
We discuss some results for the cohomology of Milnor fibers inside parameterized hypersurfaces which follow quickly from results in the category of perverse sheaves. In particular, we define a new perverse sheaf called the multiple-point complex of the parameterization, which naturally arises when investigating how the multiple-point set influences the topology of the Milnor fiber. Time Permitting, we will discuss applications to one-parameter deformations of such hypersurfaces. This is joint work with David Massey.<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14544Graduate/Postdoc Topology and Singularities Seminar2017-11-16T15:32:53Z<p>Maxim: /* 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 />
|"TBA"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14535Graduate/Postdoc Topology and Singularities Seminar2017-11-13T16:18:41Z<p>Maxim: /* 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 />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|Nov 29<br />
|Alexandra Kjuchukova <br />
|"TBA"<br />
|-<br />
|-<br />
|December 6<br />
|TBD <br />
|"TBA"<br />
|-<br />
|-<br />
|December 13<br />
|TBD <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14534Graduate/Postdoc Topology and Singularities Seminar2017-11-13T16:17:05Z<p>Maxim: /* 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 />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|-<br />
|-<br />
|Nov 29<br />
|Alexandra Kjuchukova <br />
|"TBA"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14533Graduate/Postdoc Topology and Singularities Seminar2017-11-13T16:15:08Z<p>Maxim: /* 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 />
|Laurentiu Maxim <br />
|"Stratified Morse Theory: an overview (II)"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=14514Graduate/Postdoc Topology and Singularities Seminar2017-11-09T03:56:15Z<p>Maxim: /* 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"<br />
|}<br />
<br />
== Spring 2017==<br />
Fridays at 11:00 VV901<br />
<br />
The Seminar meets on Fridays at 11:00 pm in Van Vleck 901, and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan 27<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation I"<br />
|-<br />
|Feb 3<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation II"<br />
|-<br />
|Feb 10<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number I"<br />
|-<br />
|Feb 17<br />
|Sashka <br />
|"The Wirtinger Number of a knot equals its bridge number II"<br />
|-<br />
|Feb 24<br />
|Christian Geske <br />
|"Intersection Spaces and Equivariant Moore Approximation III"<br />
|-<br />
|Mar 3<br />
|Manuel Gonzalez Villa <br />
|"Multiplier ideals of irreducible plane curve singularities"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14319Colloquia/Fall182017-10-09T14:32:43Z<p>Maxim: /* Fall Abstracts */</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 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 />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[# October 13: Tomoko L. Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|Robert Laugwitz (Rutgers)<br />
|[[# TBA| TBA ]]<br />
|Dima Arinkin<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14318Colloquia/Fall182017-10-09T14:30:23Z<p>Maxim: /* Fall 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 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 />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[# October 13: Tomoko L. Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|Robert Laugwitz (Rutgers)<br />
|[[# TBA| TBA ]]<br />
|Dima Arinkin<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=14317Geometry and Topology Seminar2017-10-09T14:27:00Z<p>Maxim: /* 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 />
|[[#Sebastian Baader| "A filtration of the Gordian complex via symmetric groups"]]<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]<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 />
|[[#Brian Hepler| "Perverse Results on Parameterized Hypersurfaces"]]<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 />
"Hausdorff stability of round spheres under small-entropy perturbation"<br />
<br />
Colding-Minicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
=== Brian Hepler ===<br />
"Perverse Results on Parameterized Hypersurfaces"<br />
<br />
We discuss some results for the cohomology of Milnor fibers inside parameterized hypersurfaces which follow quickly from results in the category of perverse sheaves. In particular, we define a new perverse sheaf called the multiple-point complex of the parameterization, which naturally arises when investigating how the multiple-point set influences the topology of the Milnor fiber. Time Permitting, we will discuss applications to one-parameter deformations of such hypersurfaces. This is joint work with David Massey.<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=14316Geometry and Topology Seminar2017-10-09T14:25:53Z<p>Maxim: /* 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 />
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]<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 />
|[[#Brian Hepler| "Perverse Results on Parameterized Hypersurfaces"]]<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 />
"Hausdorff stability of round spheres under small-entropy perturbation"<br />
<br />
Colding-Minicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=14206Geometry and Topology Seminar2017-09-22T17:46:36Z<p>Maxim: /* 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 />
|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 />
<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=13986Geometry and Topology2017-08-29T18:28:13Z<p>Maxim: /* Conferences */</p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Topology of complex algebraic varieties<br />
<br />
[http://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT 2011) <br />
Geometric partial differential equations.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova] (U Penn 2015)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=13985Geometry and Topology2017-08-29T18:26:02Z<p>Maxim: /* Faculty */</p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Topology of complex algebraic varieties<br />
<br />
[http://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT 2011) <br />
Geometric partial differential equations.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova] (U Penn 2015)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13645Algebraic Geometry Seminar Spring 20172017-04-10T21:09:20Z<p>Maxim: /* Laurentiu Maxim */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).<br />
<br />
===Laurentiu Maxim===<br />
<br />
'''Characteristic classes of complex hypersurfaces and multiplier ideals'''<br />
<br />
I will discuss two different ways to measure the complexity of singularities of a (globally-defined) complex hypersurface. The first is derived via (Hodge-theoretic) characteristic classes of singular complex algebraic varieties, while the second is provided by the multiplier ideals. I will also point out a natural connection between these two points of view. (Joint work with Morihiko Saito and Joerg Schuermann.)</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13644Algebraic Geometry Seminar Spring 20172017-04-10T21:08:00Z<p>Maxim: /* Laurentiu Maximr */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).<br />
<br />
===Laurentiu Maxim===<br />
<br />
'''Characteristic classes of complex hypersurfaces and multiplier ideals'''<br />
<br />
I will discuss two different ways to measure the complexity of singularities of a (globally-defined) complex hypersurface. The first is derived via (Hodge-theoretic) characteristic classes of singular complex algebraic varieties, while the second is provided by the multiplier ideals. I will also point out a natural connection between these two points of view. (Join work with Morihiko Saito and Joerg Schuermann.)</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13643Algebraic Geometry Seminar Spring 20172017-04-10T21:07:16Z<p>Maxim: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).<br />
<br />
===Laurentiu Maximr===<br />
<br />
'''Characteristic classes of complex hypersurfaces and multiplier ideals'''<br />
<br />
I will discuss two different ways to measure the complexity of singularities of a (globally-defined) complex hypersurface. The first is derived via (Hodge-theoretic) characteristic classes of singular complex algebraic varieties, while the second is provided by the multiplier ideals. I will also point out a natural connection between these two points of view.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13642Algebraic Geometry Seminar Spring 20172017-04-10T20:59:29Z<p>Maxim: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).<br />
<br />
===Laurentiu Maximr===<br />
<br />
'''Characteristic classes of hypersurfaces'''<br />
<br />
Let</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13586Algebraic Geometry Seminar Spring 20172017-03-31T02:49:31Z<p>Maxim: /* Spring 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13585Algebraic Geometry Seminar Spring 20172017-03-31T02:48:05Z<p>Maxim: /* Spring 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim|TBA]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13584Algebraic Geometry Seminar Spring 20172017-03-31T02:47:45Z<p>Maxim: /* Spring 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim|TBA]]<br />
|local<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13583Algebraic Geometry Seminar Spring 20172017-03-31T02:47:16Z<p>Maxim: /* Spring 2017 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | 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 />
== Spring 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 />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|http://www.math.wisc.edu/~maxim/ Laurentiu Maxim<br />
|[[#Laurentiu Maxim|TBA]]<br />
|local<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|TBA]]<br />
|local<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13499Colloquia/Fall182017-03-13T03:24:27Z<p>Maxim: /* 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 />
== 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 />
|'''Monday, January 9, 9th floor'''<br />
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)<br />
|[[#Monday, January 9: Miklos Racz (Microsoft) | ''Statistical inference in networks and genomics'' ]]<br />
| Valko<br />
|<br />
|-<br />
|January 13, B239<br />
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)<br />
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) | ''Two dimensional water waves'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|'''Tuesday, January 17, B139'''<br />
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)<br />
|[[#Tuesday, January 17: Fabio Pusateri (Princeton) | ''The Water Waves problem'' ]]<br />
| Angenent<br />
|<br />
|-<br />
|January 20, B239<br />
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)<br />
|[[#Friday, January 20: Sam Raskin (MIT) | Tempered local geometric Langlands ]]<br />
| Arinkin<br />
|<br />
|-<br />
|'''Monday, January 23, B239'''<br />
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)<br />
|[[#Monday, January 23: Tamas Darvas (Maryland) | Geometry on the space of Kahler metrics and applications to canonical metrics ]]<br />
| Viaclovsky<br />
|<br />
|-<br />
|January 27<br />
|Reserved for possible job talks <br />
|[[# | ]]<br />
| <br />
|<br />
|-<br />
|February 3, 9th floor<br />
| Melanie Matchett Wood (UW-, Madison)<br />
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]<br />
|<br />
|<br />
|-<br />
|Monday, February 6, B239 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture), B239<br />
| Alina Chertock (NC State Univ.)<br />
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17, 9th floor<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
| [[#Friday, February 17: Gustavo Ponce(UCSB) | The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]] <br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|Monday, February 20, 9th floor<br />
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)<br />
| [[#Monday, February 20, Amy Cochran (Michigan) | Mathematical Classification of Bipolar Disorder ]]<br />
| Smith<br />
|<br />
|-<br />
|February 24<br />
| <br />
| | <br />
| <br />
|<br />
|-<br />
|March 3, B239<br />
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)<br />
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]<br />
|Dymarz<br />
|<br />
|-<br />
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Tuesday, March 7: Roger Temam (Indiana University) | On the mathematical modeling of the humid atmosphere ]]<br />
|Smith<br />
|<br />
|-<br />
|'''Wednesday, March 8, 4PM, B239 '''<br />
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University) <br />
|[[#Wednesday, March 8: Roger Temam (Indiana University) | Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]<br />
|Smith<br />
|<br />
|-<br />
|March 10<br />
| '''No Colloquium''' <br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 15, 4PM '''<br />
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)<br />
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]<br />
| Jin & Minh-Binh Tran<br />
|<br />
|-<br />
|March 17<br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| p-torsion in class groups of number fields of arbitrary degree<br />
| M. Matchett Wood<br />
|<br />
|-<br />
|March 24<br />
| '''Spring Break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Wednesday, March 29 at 3:30PM (Wasow)'''<br />
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU) <br />
|[[# Wednesday, March 29 at 3:30PM (Wasow)| Microscopic description of Coulomb-type systems ]]<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 />
| <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 />
==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 />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<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 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <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 />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <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 />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<br />
<br />
=== Monday, December 19: Andrew Zimmer (U Chicago) ===<br />
''Metric spaces of non-positive curvature and applications in several complex variables''<br />
<br />
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.<br />
<br />
=== Monday, January 9: Miklos Racz (Microsoft) ===<br />
''Statistical inference in networks and genomics''<br />
<br />
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas. <br />
<br />
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.<br />
<br />
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===<br />
''Two dimensional water waves''<br />
<br />
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.<br />
<br />
=== Tuesday, January 17: Fabio Pusateri (Princeton) ===<br />
''The Water Waves problem''<br />
<br />
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.<br />
<br />
=== Friday, January 20: Sam Raskin (MIT) === <br />
''Tempered local geometric Langlands ''<br />
<br />
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.<br />
<br />
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.<br />
<br />
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.<br />
<br />
=== Monday, January 23: Tamas Darvas (Maryland) ===<br />
''Geometry on the space of Kahler metrics and applications to canonical metrics''<br />
<br />
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler<br />
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are<br />
minimizers of well known functionals on the space of all Kahler metrics H. However these<br />
functionals become convex only if an adequate geometry is chosen on H. One such choice of<br />
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of<br />
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on<br />
H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give<br />
applications related to existence of special Kahler metrics, including the recent resolution of<br />
Tian's related properness conjectures. <br />
<br />
<br />
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===<br />
''Random groups from generators and relations''<br />
<br />
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations. We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen. Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. <br />
<br />
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===<br />
''Models for neural networks; analysis, simulations and behaviour''<br />
<br />
Neurons exchange informations via discharges, propagated <br />
by membrane potential, which trigger firing of the many connected <br />
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?<br />
How can such a network generate a spontaneous activity? <br />
Such questions can be tackled using nonlinear integro-differential <br />
equations. These are now classically used in the neuroscience community to describe <br />
neuronal networks or neural assemblies. Among them, the best known is certainly <br />
Wilson-Cowan's equation which <br />
describe spiking rates arising in different brain locations. <br />
<br />
Another classical model is the integrate-and-fire equation that describes <br />
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state, <br />
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed. <br />
<br />
One can also describe directly the spike time <br />
distribution which seems to encode more directly the neuronal information. <br />
This leads to a structured population equation that describes <br />
at time $t$ the probability to find a neuron with time $s$ <br />
elapsed since its last discharge. Here, we can <br />
show that small or large connectivity <br />
leads to desynchronization. For intermediate regimes, sustained <br />
periodic activity occurs. <br />
A common mathematical tool is the use of the relative entropy method.<br />
<br />
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.<br />
<br />
=== February 10: Alina Chertock (NC State Univ.) ===<br />
''Numerical Method for Chemotaxis and Related Models''<br />
<br />
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.<br />
<br />
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.<br />
<br />
<br />
=== Friday, February 17: Gustavo Ponce(UCSB) ===<br />
<br />
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''<br />
<br />
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation<br />
<br />
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math><br />
<br />
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation<br />
<br />
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math><br />
<br />
where <math>\mathcal {H}</math> denotes the Hilbert transform,<br />
<br />
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math><br />
<br />
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.<br />
<br />
These include a comparison of the local and global well-posedness and unique continuation properties <br />
as well as special features of the special solutions of these models.<br />
<br />
=== Monday, February 20, Amy Cochran (Michigan) ===<br />
''Mathematical Classification of Bipolar Disorder''<br />
<br />
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.<br />
<br />
=== Friday, March 3, Ken Bromberg (Utah)===<br />
"Renormalized volume for hyperbolic 3-manifolds"<br />
<br />
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.<br />
<br />
=== Tuesday, March 7: Roger Temam (Indiana University) ===<br />
''On the mathematical modeling of the humid atmosphere''<br />
<br />
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.<br />
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.<br />
<br />
=== Wednesday, March 8: Roger Temam (Indiana University) ===<br />
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''<br />
<br />
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.<br />
Based on an article with Du Pham, to appear in Nonlinear Analysis.<br />
<br />
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===<br />
''Control and numerics: Recent progress and challenges''<br />
<br />
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.<br />
<br />
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.<br />
<br />
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.<br />
<br />
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:<br />
<br />
- Inverse design for hyperbolic conservation laws,<br />
<br />
- The turnpike property: control in long time intervals,<br />
<br />
- Collective behavior: guidance by repulsion.<br />
<br />
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.<br />
<br />
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.<br />
<br />
<br />
===Friday, March 17 at 4:00pm: Lillian Pierce (Duke)===<br />
''P-torsion in class groups of number fields of arbitrary degree''<br />
<br />
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.<br />
<br />
=== Wednesday, March 29 at 3:30PM (Wasow): Sylvia Serfaty (NYU)===<br />
''Microscopic description of Coulomb-type systems''<br />
<br />
We are interested in systems of points with Coulomb, logarithmic<br />
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens<br />
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau<br />
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named<br />
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.<br />
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.<br />
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13128Graduate/Postdoc Topology and Singularities Seminar2017-01-25T18:21:39Z<p>Maxim: </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 />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13017Graduate/Postdoc Topology and Singularities Seminar2017-01-17T03:33:32Z<p>Maxim: </p>
<hr />
<div>== Spring 2017==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 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. 25<br />
|Christian Geske <br />
|"TBA"<br />
|-<br />
|}<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=13016Graduate/Postdoc Topology and Singularities Seminar2017-01-17T03:32:50Z<p>Maxim: </p>
<hr />
<div>== Spring 2017==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 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. 25<br />
|Christian Geske <br />
|"TBA"<br />
|-<br />
<br />
== Fall 2016==<br />
Wednesdays at 14:30 VV901<br />
<br />
The Seminar meets on Wednesdays at 14:30 pm in Van Vleck 901 (except on October 26th when we will meet in Van Vleck 903), and is coordinated by Alexandra Kjuchukova, Manuel Gonzalez Villa and Botong Wang.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 14 (W)<br />
|Laurentiu Maxim <br />
|"Alexander-type invariants of hypersurface complements"<br />
|-<br />
|Sept. 21 (W)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|Sept. 28 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"Introduction to Newton polyhedra"<br />
|-<br />
|Oct 12 (W)<br />
|Manuel Gonzalez Villa <br />
|"More on Newton polyhedra"<br />
|-<br />
|Oct 26 (W)<br />
|Christian Geske<br />
|"Intersection Spaces"<br />
|-<br />
|Nov 2 (W)<br />
|Christian Geske<br />
|"Intersection Spaces Continued"<br />
|-<br />
|Nov 9 (W)<br />
|CANCELLED<br />
|-<br />
|Nov 16 (W)<br />
|Eva Elduque<br />
|"Braids and the fundamental group of plane curve complements"<br />
|-<br />
|Nov 30 (W)<br />
|Laurentiu Maxim<br />
|"Novikov homology of hypersurface complements"<br />
|-<br />
|Dec 7 (W)<br />
|CANCELLED<br />
|-<br />
|Dec 14 (W)<br />
|Eva Elduque<br />
|Specialty Exam: "Twisted Alexander invariants of plane curve complements"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12964Geometry and Topology Seminar2017-01-11T21:54:16Z<p>Maxim: /* 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 />
| <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 />
| <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 />
|[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 />
== 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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12963Geometry and Topology Seminar2017-01-11T21:52:56Z<p>Maxim: /* 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 />
| <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 />
|[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 />
===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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12808Graduate/Postdoc Topology and Singularities Seminar2016-12-06T19:24:22Z<p>Maxim: /* 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 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<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12788Colloquia/Fall182016-11-30T21:52:05Z<p>Maxim: /* Abstracts */</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 />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<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 />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([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 />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Monday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<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 />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<br />
| Minh-Binh Tran<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://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<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 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <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 />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <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 />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
===Monday, December 5: Botong Wang (UW-Madison)===<br />
Title: Enumeration of points, lines, planes, etc.<br />
<br />
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12787Colloquia/Fall182016-11-30T21:50:15Z<p>Maxim: /* 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 />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<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 />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([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 />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Monday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<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 />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<br />
| Minh-Binh Tran<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://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<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 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <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 />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <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 />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12786Colloquia/Fall182016-11-30T21:49:24Z<p>Maxim: /* 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 />
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<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 />
|Hypergeometric functions over finite fields<br />
| Yang<br />
|<br />
|-<br />
|October 21<br />
|'''No colloquium this week'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|'''Tuesday, October 25, 9th floor'''<br />
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)<br />
|Three Miracles in Analysis<br />
|Seeger<br />
|<br />
|-<br />
|October 28, 9th floor<br />
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)<br />
|Microscopic hydrodynamic modes in a binary mixture<br />
|Minh-Binh Tran<br />
|<br />
|-<br />
|'''Monday, October 31, B239'''<br />
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)<br />
|Groups acting on the circle<br />
|Smith<br />
|<br />
|-<br />
|November 4<br />
|<br />
|<br />
| <br />
|<br />
|-<br />
|'''Monday, November 7 at 4:30, 9th floor''' ([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 />
|'''Wednesday, November 16, 9th floor'''<br />
| [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)<br />
|Shapes of Julia Sets<br />
|Michell<br />
|<br />
|-<br />
|November 18, B239<br />
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)<br />
|Recent progress in representation stability<br />
|Ellenberg<br />
|<br />
|-<br />
|'''Monday, November 21, 9th floor'''<br />
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)<br />
|Definability in degree structures<br />
|Smith<br />
|<br />
|-<br />
|November 25<br />
| '''Thanksgiving break'''<br />
|[[# | ]]<br />
|<br />
|<br />
|-<br />
|December 2, 9th floor<br />
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)<br />
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]<br />
|Roch<br />
|<br />
|-<br />
|'''Monday, December 5, B239'''<br />
| [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)<br />
|[[#Friday, December 5: Botong Wang (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]<br />
|Maxim<br />
|<br />
|-<br />
|December 9, B239<br />
| [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)<br />
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]<br />
|Kent<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 />
|-<br />
|February 6 (Wasow lecture)<br />
| Benoit Perthame (University of Paris VI)<br />
|[[# TBA| TBA ]] <br />
| Jin<br />
| <br />
|-<br />
|February 10 (WIMAW lecture)<br />
| Alina Chertock (NC State Univ.)<br />
|[[# | ]] <br />
| WIMAW<br />
|<br />
|-<br />
|February 17<br />
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)<br />
|[[# | ]]<br />
| Minh-Binh Tran<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://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) <br />
| TBA<br />
| M. Matchett Wood<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 23: Gheorghe Craciun (UW-Madison) ===<br />
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture<br />
<br />
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. <br />
<br />
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.<br />
<br />
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. <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 />
=== October 14: Ling Long (LSU) === <br />
Title: Hypergeometric functions over finite fields<br />
<br />
Abstract: Hypergeometric functions are special functions with lot of<br />
symmetries. In this talk, we will introduce hypergeometric functions over finite<br />
fields, originally due to Greene, Katz and McCarthy, in a way that is<br />
parallel to the classical hypergeometric functions, and discuss their<br />
properties and applications to character sums and the arithmetic of<br />
hypergeometric abelian varieties. <br />
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.<br />
<br />
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===<br />
Title: Three Miracles in Analysis<br />
<br />
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).<br />
<br />
=== October 28: Linda Reichl (UT Austin) ===<br />
Title: Microscopic hydrodynamic modes in a binary mixture<br />
<br />
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.<br />
<br />
===Monday, October 31: Kathryn Mann (Berkeley) ===<br />
Title: Groups acting on the circle<br />
<br />
Abstract: Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. <br />
<br />
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. <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 />
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===<br />
Title: Shapes of Julia Sets<br />
<br />
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?" For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is "yes!" I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.<br />
<br />
===November 18: Andrew Snowden (University of Michigan)===<br />
Title: Recent progress in representation stability<br />
<br />
Abstract: Representation stability is a relatively new field that studies<br />
somewhat exotic algebraic structures and exploits their properties to<br />
prove results (often asymptotic in nature) about objects of interest.<br />
I will describe some of the algebraic structures that appear (and<br />
state some important results about them), give a sampling of some<br />
notable applications (in group theory, topology, and algebraic<br />
geometry), and mention some open problems in the area.<br />
<br />
===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===<br />
Title: Definability in degree structures<br />
<br />
Abstract: Some incomputable sets are more incomputable than others. We use<br />
Turing reducibility and enumeration reducibility to measure the<br />
relative complexity of incomputable sets. By identifying sets of the<br />
same complexity, we can associate to each reducibility a degree<br />
structure: the partial order of the Turing degrees and the partial<br />
order of the enumeration degrees. The two structures are related in<br />
nontrivial ways. The first has an isomorphic copy in the second and<br />
this isomorphic copy is an automorphism base. In 1969, Rogers asked a<br />
series of questions about the two degree structures with a common<br />
theme: definability. In this talk I will introduce the main concepts<br />
and describe the work that was motivated by these questions.<br />
<br />
===Friday, December 2: Hao Shen (Columbia)===<br />
Title: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?<br />
<br />
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.<br />
<br />
=== Friday, December 9: Aaron Brown (U Chicago) ===<br />
''Lattice actions and recent progress in the Zimmer program''<br />
<br />
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. <br />
<br />
I will present some background, motivation, and selected previous results in the Zimmer program. I will then explain two of my results within the Zimmer program:<br />
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);<br />
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12768Graduate/Postdoc Topology and Singularities Seminar2016-11-28T15:15:29Z<p>Maxim: /* 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 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 />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12723Geometry and Topology Seminar2016-11-14T03:51:46Z<p>Maxim: /* 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| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<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 />
| <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 />
| [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 />
=== 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 />
''TBA''<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 />
<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12722Geometry and Topology Seminar2016-11-14T03:50:33Z<p>Maxim: /* 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| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<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 />
| <br />
| <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 />
| <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 />
| [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 />
=== 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 />
''TBA''<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 />
<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12721Geometry and Topology Seminar2016-11-14T03:50:08Z<p>Maxim: /* 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| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "TBA"]]<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 />
| <br />
| <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 />
| <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 />
| [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 />
=== 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 />
''TBA''<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 />
<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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12635Geometry and Topology Seminar2016-11-01T03:39:11Z<p>Maxim: /* Fall 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/~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<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 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| [http://www.math.wisc.edu/~rkent Richard Kent] (Wisconsin)<br />
| [[#Richard Kent| ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<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| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| <br />
| <br />
| <br />
|-<br />
|December 16<br />
| <br />
| <br />
| <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 />
=== 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 />
''TBA''<br />
<br />
=== Richard Kent ===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
Thurston's Geometrization Conjecture, now a celebrated theorem of Perelman, tells us that most 3-manifolds are naturally geometric in nature. In fact, most 3-manifolds admit hyperbolic metrics. In the 1970s, Thurston proved the Geometrization conjecture in the case of Haken manifolds, and the proof revolutionized 3-dimensional topology, hyperbolic geometry, Teichm&uuml;ller theory, and dynamics. Thurston's proof is by induction, constructing a hyperbolic structure from simpler pieces. At the heart of the proof is an analytic function called the ''skinning map'' that one must understand in order to glue hyperbolic structures together. A better understanding of this map would more brightly illuminate the interaction between topology and geometry in dimension three. I will discuss what is currently known about this map.<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<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 />
== 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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=12632Geometry and Topology Seminar2016-10-30T22:58:38Z<p>Maxim: /* Fall 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/~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<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 7''' <br />
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (University of New Zealand) <br />
| [[#Gaven Martin| "TBA"]]<br />
| Simon Marshall <br />
|-<br />
|November 11<br />
| [http://www.math.wisc.edu/~rkent Richard Kent] (Wisconsin)<br />
| [[#Richard Kent| ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "TBA"]]<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| "TBA"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Reserved<br />
| <br />
| Max<br />
|-<br />
|December 16<br />
| <br />
| <br />
| <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 />
=== 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 />
''TBA''<br />
<br />
=== Richard Kent ===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
Thurston's Geometrization Conjecture, now a celebrated theorem of Perelman, tells us that most 3-manifolds are naturally geometric in nature. In fact, most 3-manifolds admit hyperbolic metrics. In the 1970s, Thurston proved the Geometrization conjecture in the case of Haken manifolds, and the proof revolutionized 3-dimensional topology, hyperbolic geometry, Teichm&uuml;ller theory, and dynamics. Thurston's proof is by induction, constructing a hyperbolic structure from simpler pieces. At the heart of the proof is an analytic function called the ''skinning map'' that one must understand in order to glue hyperbolic structures together. A better understanding of this map would more brightly illuminate the interaction between topology and geometry in dimension three. I will discuss what is currently known about this map.<br />
<br />
=== Caglar Uyanik ===<br />
''TBA''<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 />
== 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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12437Graduate/Postdoc Topology and Singularities Seminar2016-09-30T14:48:12Z<p>Maxim: /* 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 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 />
|"TBA"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12436Graduate/Postdoc Topology and Singularities Seminar2016-09-30T14:46:15Z<p>Maxim: </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 (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 />
|"TBA"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12435Graduate/Postdoc Topology and Singularities Seminar2016-09-30T14:37:44Z<p>Maxim: /* 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 (W)<br />
|Alexandra Kjuchukova <br />
|"On the Bridge Number vs Meridional Rank Conjecture"<br />
|-<br />
|Oct 5 (W)<br />
|Manuel Gonzalez Villa <br />
|"TBA"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Graduate/Postdoc_Topology_and_Singularities_Seminar&diff=12349Graduate/Postdoc Topology and Singularities Seminar2016-09-19T16:59:06Z<p>Maxim: </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. 23 (M)<br />
|Botong Wang <br />
|"Cohomology jump loci"<br />
|-<br />
|}<br />
<br />
== Spring 2016==<br />
Mondays at 3:20 B139VV<br />
<br />
The old Graduate Singularities Seminar will meet as a Graduate/Postdoc Topology and Singularities Seminar in Fall 2015 and Spring 2016.<br />
<br />
The seminar meets on Mondays at 3:20 pm in Van Vleck B139. During Spring 2016 we will cover first chapters the book Singularities in Topology by Alex Dimca (Universitext, Springer Verlag, 2004). If you would like to participate giving one of the talks, please contact Eva Elduque or Christian Geske.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 8 (M)<br />
|Christian Geske<br />
|Section 1.1 and 1.2: ''Category of complexes and Homotopical category''<br />
|-<br />
|Feb. 15 (M)<br />
|Eva Elduque<br />
|Sections 1.3 and 1.4: ''Derived category and derived functors''<br />
|-<br />
|Feb. 22 (M)<br />
|Botong Wang<br />
|Sections 2.1 and 2.2: ''Generalities on Sheaves and Derived tensor products''<br />
|-<br />
|Feb. 29 (M)<br />
|Christian Geske<br />
|''Hypercohomology and Holomorphic Differential Forms on Analytic Varieties''<br />
|-<br />
|Mar. 7 (M)<br />
|Eva Elduque<br />
|Section 2.3: ''Direct and inverse image''<br />
|-<br />
|Mar. 14 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Mar. 28 (M)<br />
|<br />
|Cancelled <br />
|-<br />
|Apr. 4 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 11 (M)<br />
|Christian Geske<br />
|Section 2.3 cont.<br />
|-<br />
|Apr. 18 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|Apr. 25 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|May. 2 (M)<br />
|<br />
|Cancelled<br />
|-<br />
|}<br />
<br />
If you would like to present a topic, please contact Eva Elduque or Christian Geske.<br />
<br />
== Abstracts ==<br />
<br />
<br />
(From the back cover of Dimca's book) Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).<br />
<br />
This introduction to the subject can be regarded as a textbook on Modern Algebraic Topology, which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).<br />
<br />
The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.<br />
<br />
Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.<br />
<br />
== Fall 2015 ==<br />
<br />
Thursdays 4pm in B139VV<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 24 (Th)<br />
|KaiHo (Tommy) Wong<br />
|''Twisted Alexander Invariant for Knots and Plane Curves''<br />
|-<br />
|Oct. 1 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers I''<br />
|-<br />
|Oct. 8 (Th)<br />
|Alexandra (Sashka) Kjuchukova<br />
|''Linking numbers and branched covers II''<br />
|-<br />
|Oct. 15 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture I''<br />
|-<br />
|Oct. 22 (Th)<br />
|Yun Su (Suky)<br />
|Pretalk ''Higher-order degrees of hypersurface complements.'', Survey on Alexander polynomial for plane curves.<br />
|-<br />
|Oct. 29 (Th)<br />
|Yun Su (Suky)<br />
|Aftertalk ''Higher-order degrees of hypersurface complements.''<br />
|-<br />
|Nov. 5 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture II''<br />
|-<br />
|Nov. 12 (Th)<br />
|Manuel Gonzalez Villa<br />
|''On poles of zeta functions and monodromy conjecture III''<br />
|-<br />
|Nov. 19 (Th)<br />
|Eva Elduque<br />
|''Stiefel-Whitney classes''<br />
|-<br />
|Dec. 3 (Th)<br />
|Eva Elduque<br />
|''Grass-mania!''<br />
|-<br />
|Dec. 10 (Th)<br />
|KaiHo (Tommy) Wong<br />
|Pretalk ''Milnor Fiber of Complex Hyperplane Arrangements''<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Th, Sep 24: Tommy===<br />
Twisted Alexander Invariant of Knots and Plane Curves.<br />
<br />
I will introduced three invariants of knots and plane curves, fundamental group, Alexander polynomial, and twisted Alexander polynomial. Some basic examples will be used to illustrate how Alexander polynomial or twisted Alexander polynomial can be computed from the fundamental group. If time permits, I will survey some known facts about twisted Alexander invariant of plane curves.<br />
<br />
<br />
===Th, Oct 1 and 8: Sashka===<br />
Linking numbers and branched coverings I and II<br />
<br />
Let K be a knot in S^3, and let M be a non-cyclic branched cover of S^3 with branching set K. The linking numbers between the branch curves in M, when defined, are an invariant of K which can be traced back to Reidemeister and was used by Ken Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent work in the study of branched covers of four-manifolds with singular branching sets leads us to consider the linking of other curves in M besides the branch curves. <br />
<br />
In these two talks, I will outline Perko's original method for computing linking in a branched cover, and I will give a brief overview of its classical applications. Then, I'll describe a suitable generalization of his method, and explain its relevance to a couple of open questions in the classification of branched covers between four-manifolds.<br />
<br />
===Th, Oct 15, Nov 5 and Nov 12: Manuel===<br />
On poles of zeta functions and monodromy conjecture I and II<br />
<br />
Brief introduction to topological and motivic zeta functions and their relations. Statement of the monodromy conjecture. Characterization and properties of poles of the in the case of plane curves. Open problems in the case of quasi-ordinary singularities.<br />
<br />
===Th, Nov 19: Eva===<br />
Stiefel-Whitney classes<br />
<br />
Not all elements in the Z_2 cohomology ring of the base space of a real vector bundle are created equal. We will define the Stiefel-Whitney classes and give evidence of why they are the cool kids of the cohomology dance. For example, they will tell us information about when a manifold is the boundary of another one or when we can’t embed a given projective space into R^n.<br />
<br />
===Th, Dec 3: Eva===<br />
Grass-mania!<br />
<br />
In this talk, we will talk about the grassmannians, both the finite and infinite dimensional ones. We will define their canonical vector bundles, which turn out to be universal in some sense, and give them a CW structure to compute their cohomology ring. As an application, we will prove the uniqueness of the Stiefel-Whitney classes defined in the last talk.<br />
<br />
This talk is for the most part self contained, so it doesn't matter if you missed the previous one.<br />
<br />
<br />
===Th, Dec 10: Tommy===<br />
<br />
A line is one of the simplest geometric objects, but a whole bunch of them could provide us open problems!<br />
<br />
I will talk about some past results on line arrangements, that are whole bunches of lines. I will speak a little bit on why line arrangements or plane arrangements stand out from other hypersurfaces in the study of topological singularity theory.<br />
<br />
== Spring 2014 ==<br />
<br />
We continue with Professor Alex Suciu's work.<br />
<br />
== Fall 2014 ==<br />
<br />
We follow Professor Alex Suciu's work this semester.<br />
<br />
http://www.northeastern.edu/suciu/publications.html<br />
<br />
But we will not meet at a regular basis.<br />
<br />
<br />
== Spring 2014 ==<br />
<br />
We meet on Tuesdays 3:30-4:25pm in room B211.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 25 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition I''<br />
|-<br />
|Mar. 4 (Tue)<br />
|Yongqiang Liu<br />
|''Monodromy Decomposition II''<br />
|-<br />
|Mar. 25 (Tue)<br />
|KaiHo Wong<br />
|''Conjecture of lower bounds of Alexander polynomial''<br />
|-<br />
|Apr. 8 (Tue)<br />
|Yongqiang Liu<br />
|''Nearby Cycles and Alexander Modules''<br />
|-<br />
|}<br />
<br />
== Fall 2013 ==<br />
<br />
We are learning Hodge Theory this semester and will be following three books:<br />
<br />
1. Voisin, Hodge Theory and Complex Algebraic Geometry I & II<br />
<br />
2. Peters, Steenbrink, Mixed Hodge Structures <br />
<br />
We meet weekly on Wednesdays from 12 at noon to 1pm in room 901.<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 18 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Sep. 25 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor Fibration at infinity of polynomial map''<br />
|-<br />
|Oct. 9 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|-<br />
|Oct. 16 (Wed)<br />
|Yongqiang Liu<br />
|''Polynomial singularities''<br />
|-<br />
|Nov. 13 (Wed)<br />
|KaiHo Wong<br />
|Discussions on book material<br />
|}<br />
<br />
== Spring 2013 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Feb. 6 (Wed)<br />
|Jeff Poskin<br />
|''Toric Varieties III''<br />
|-<br />
|Feb.13 (Wed)<br />
|Yongqiang Liu<br />
|''Intersection Alexander Module''<br />
|-<br />
|Feb.20 (Wed)<br />
|Yun Su (Suky)<br />
|''How do singularities change shape and view of objects?''<br />
|-<br />
|Feb.27 (Wed)<br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements''<br />
|-<br />
|Mar.20 (Wed)<br />
|J&ouml;rg Sch&uuml;rmann (University of M&uuml;nster, Germany)<br />
|''Characteristic classes of singular toric varieties''<br />
|-<br />
|Apr. 3 (Wed) <br />
|KaiHo Wong<br />
|''Fundamental groups of plane curves complements II''<br />
|-<br />
|Apr.10 (Wed)<br />
|Yongqiang Liu<br />
|''Milnor fiber of local function germ''<br />
|-<br />
|Apr.17 (Wed) 2:45pm-3:45pm (Note the different time)<br />
|KaiHo Wong<br />
|''Formula of Alexander polynomials of plane curves''<br />
|-<br />
|-<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Wed, 2/27: Tommy===<br />
''Fundamental groups of plane curves complements''<br />
<br />
I will sketch the proof of the Zariski-Van Kampen thereon and say some general results about the fundamental groups of plane curves complements. In particular, we will investigate, under what conditions, these groups are abelian. Some simple examples will be provided. And if time permits, some classical examples of Zariski and Oka will be computed. <br />
<br />
<br />
<br />
<br />
== Fall 2012 ==<br />
<br />
{| cellpadding="5"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 18 (Tue)<br />
|KaiHo Wong <br />
|Organization and ''Milnor fibration and Milnor Fiber''<br />
|-<br />
|Sept. 25 (Tue)<br />
|KaiHo Wong <br />
|''Algebraic links and exotic spheres''<br />
|-<br />
|Oct. 4 (Thu)<br />
|Yun Su (Suky)<br />
|''Alexander polynomial of complex algebraic curve'' (Note the different day but same time and location)<br />
|-<br />
|Oct. 11 (Thu)<br />
|Yongqiang Liu<br />
|''Sheaves and Hypercohomology''<br />
|-<br />
|Oct. 18 (Thu)<br />
|Jeff Poskin<br />
|''Toric Varieties II''<br />
|-<br />
|Nov. 1 (Thu)<br />
|Yongqiang Liu<br />
|''Mixed Hodge Structure''<br />
|-<br />
|Nov. 15 (Thu)<br />
|KaiHo Wong<br />
|''Euler characteristics of hypersurfaces with isolated singularities''<br />
|-<br />
|Nov. 29 (Thu)<br />
|Markus Banagl, University of Heidelberg<br />
|''High-Dimensional Topological Field Theory, Automata Theory, and Exotic spheres''<br />
|-<br />
|}<br />
== Abstracts ==<br />
<br />
===Thu, 10/4: Suky===<br />
''Alexander polynomial of complex algebraic curve''<br />
<br />
I will extend the definition of Alexander polynomial in knot theory to an complex algebraic curve. <br />
From the definition, it is clear that Alexander polynomial is an topological invariant for curves.<br />
I will explain how the topology of a curve control its Alexander polynomial, in terms of the factors. <br />
Calculations of some examples will be provided.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=12261Colloquia/Fall182016-09-09T20:02:08Z<p>Maxim: </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 />
| <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>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Tentative_Colloquia&diff=11676Tentative Colloquia2016-03-24T15:30:17Z<p>Maxim: /* tentative Schedule Spring 2016 */</p>
<hr />
<div>= tentative Schedule Spring 2016 =<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 />
|September 16<br />
| ( )<br />
|[[# | ]]<br />
| <br />
|-<br />
|September 23<br />
| ( )<br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
| TBA (TBA)<br />
|[[# TBA| TBA ]] <br />
| Hung Tran <br />
|-<br />
|October 7<br />
| [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook) <br />
|[[# TBA | TBA ]]<br />
| Maxim<br />
|-<br />
|October 14<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|October 21<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|October 28<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 4<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 11<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 18<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 25<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|December 2<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|December 9<br />
| ( )<br />
|[[# | ]]<br />
|</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Tentative_Colloquia&diff=11675Tentative Colloquia2016-03-24T15:27:00Z<p>Maxim: /* tentative Schedule Spring 2016 */</p>
<hr />
<div>= tentative Schedule Spring 2016 =<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 />
|September 16<br />
| ( )<br />
|[[# | ]]<br />
| <br />
|-<br />
|September 23<br />
| ( )<br />
|[[# | ]]<br />
| <br />
|-<br />
|September 30<br />
| TBA (TBA )<br />
|[[# TBA| TBA ]] <br />
| Hung Tran <br />
|-<br />
|October 7<br />
| TBA ( TBA )<br />
|[[# | ]]<br />
| Maxim<br />
|-<br />
|October 14<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|October 21<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|October 28<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 4<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 11<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 18<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|November 25<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|December 2<br />
| ( )<br />
|[[# | ]]<br />
|<br />
|-<br />
|December 9<br />
| ( )<br />
|[[# | ]]<br />
|</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2015&diff=10357Algebraic Geometry Seminar Fall 20152015-09-29T18:52:35Z<p>Maxim: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B223.<br />
<br />
The schedule for the previous semester is [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar_Spring_2015 here].<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 2015 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 18<br />
|[http://www.math.harvard.edu/~ebriedl/ Eric Riedl] (UIC)<br />
|Rational Curves on Hypersurfaces<br />
|Jordan<br />
|-<br />
|September 25<br />
|[http://www.mathcs.emory.edu/~dzb/ David Zureick-Brown] (Emory)<br />
|Hilbert schemes of canonically embedded curves of low genus<br />
|Jordan<br />
|-<br />
|October 2<br />
|[https://math.temple.edu/~vald/ Vasily Dolgushev] (Temple)<br />
|A manifestation of the Grothendieck-Teichmueller group in geometry<br />
|Andrei<br />
|-<br />
|October 9<br />
|[https://math.wisc.edu/~maxim/ Laurentiu Maxim] (Madison)<br />
|Equivariant invariants of external and symmetric products of quasi-projective varieties<br />
|local<br />
|-<br />
|October 16<br />
|[http://www.math.wisc.edu/~dewey/ Ed Dewey] (Madison)<br />
|TBA<br />
|local<br />
|-<br />
|October 23<br />
|[http://people.math.sc.edu/kassj/ Jesse Kass] (South Carolina)<br />
|How to count zeros arithmetically?<br />
|Melanie<br />
|-<br />
|November 13<br />
|[http://www-personal.umich.edu/~jakelev/ Jake Levinson] (Michigan)<br />
|TBA<br />
|Daniel<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Eric Riedl===<br />
Rational Curves on Hypersurfaces<br />
<br />
One way to understand the geometry of a variety is to understand its rational curves. Even for some relatively simple varieties, little is known about their spaces of rational curves. Many people have made previous progress on these questions, but there remain many open cases. In joint work with David Yang, we investigate the dimensions of the spaces of rational curves on very general hypersurfaces, and prove that for n > d+1 or d > (3n+1)/2, the spaces of rational curves have the expected dimension, as conjectured (in various cases) by several people, including Coskun, Harris and Starr, and Voisin. In this talk, we focus our attention particularly on the Fano case and try to motivate some of the ideas used to attack this problem.<br />
<br />
===David Zureick-Brown===<br />
Hilbert schemes of canonically embedded curves of low genus<br />
<br />
I'll discuss new work (joint with Aaron Landesman) on smoothability of low genus curves.<br />
<br />
===Jess Kass===<br />
How to count zeros arithmetically?<br />
<br />
A celebrated result of Eisenbud--Kimshaishvili--Levine computes the local Brouwer degree of a real polynomial function at an isolated zero as the signature of a quadratic form. I will discuss a parallel result in A1-homotopy theory, and time permitting, explain how to study a singularity by applying these results to the gradient of a defining equation. This is joint work with Kirsten Wickelgren.<br />
<br />
===Vasily Dolgushev===<br />
A manifestation of the Grothendieck-Teichmueller group in geometry<br />
<br />
Inspired by Grothendieck’s lego-game, Vladimir Drinfeld introduced, in<br />
1990, the Grothendieck-Teichmueller group GRT. This group has<br />
interesting links to the absolute Galois group of rationals, moduli of<br />
algebraic curves, solutions of the Kashiwara-Vergne problem, and<br />
theory of motives. My talk will be devoted to the manifestation of GRT<br />
in the extended moduli of algebraic varieties, which was conjectured<br />
by Maxim Kontsevich in 1999. My talk is partially based on the joint<br />
paper with Chris Rogers and Thomas Willwacher: http://arxiv.org/abs/1211.4230.<br />
<br />
===Laurentiu Maxim===<br />
Equivariant invariants of external and symmetric products of quasi-projective varieties<br />
<br />
I will start by revisiting formulae for the generating series of genera of symmetric products (with suitable coefficients), <br />
which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical <br />
results in the literature as special cases. Important specializations of these results include generating series for <br />
extensions of Hodge numbers and Hirzebruch genus to the singular setting and, in particular, generating series <br />
for intersection cohomology Hodge numbers and Goresky-MacPherson intersection cohomology signatures <br />
of symmetric products of complex projective varieties. In the second part of the talk, I will describe a generating series formula<br />
for equivariant invariants of external products, which includes all of the above-mentioned results as special cases.<br />
This is joint work with Joerg Schuermann.</div>Maximhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2015&diff=10356Algebraic Geometry Seminar Fall 20152015-09-29T18:51:40Z<p>Maxim: /* Fall 2015 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B223.<br />
<br />
The schedule for the previous semester is [https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar_Spring_2015 here].<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 2015 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 18<br />
|[http://www.math.harvard.edu/~ebriedl/ Eric Riedl] (UIC)<br />
|Rational Curves on Hypersurfaces<br />
|Jordan<br />
|-<br />
|September 25<br />
|[http://www.mathcs.emory.edu/~dzb/ David Zureick-Brown] (Emory)<br />
|Hilbert schemes of canonically embedded curves of low genus<br />
|Jordan<br />
|-<br />
|October 2<br />
|[https://math.temple.edu/~vald/ Vasily Dolgushev] (Temple)<br />
|A manifestation of the Grothendieck-Teichmueller group in geometry<br />
|Andrei<br />
|-<br />
|October 9<br />
|[https://math.wisc.edu/~maxim/ Laurentiu Maxim] (Madison)<br />
|Equivariant invariants of external and symmetric products of quasi-projective varieties<br />
|local<br />
|-<br />
|October 16<br />
|[http://www.math.wisc.edu/~dewey/ Ed Dewey] (Madison)<br />
|TBA<br />
|local<br />
|-<br />
|October 23<br />
|[http://people.math.sc.edu/kassj/ Jesse Kass] (South Carolina)<br />
|How to count zeros arithmetically?<br />
|Melanie<br />
|-<br />
|November 13<br />
|[http://www-personal.umich.edu/~jakelev/ Jake Levinson] (Michigan)<br />
|TBA<br />
|Daniel<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Eric Riedl===<br />
Rational Curves on Hypersurfaces<br />
<br />
One way to understand the geometry of a variety is to understand its rational curves. Even for some relatively simple varieties, little is known about their spaces of rational curves. Many people have made previous progress on these questions, but there remain many open cases. In joint work with David Yang, we investigate the dimensions of the spaces of rational curves on very general hypersurfaces, and prove that for n > d+1 or d > (3n+1)/2, the spaces of rational curves have the expected dimension, as conjectured (in various cases) by several people, including Coskun, Harris and Starr, and Voisin. In this talk, we focus our attention particularly on the Fano case and try to motivate some of the ideas used to attack this problem.<br />
<br />
===David Zureick-Brown===<br />
Hilbert schemes of canonically embedded curves of low genus<br />
<br />
I'll discuss new work (joint with Aaron Landesman) on smoothability of low genus curves.<br />
<br />
===Jess Kass===<br />
How to count zeros arithmetically?<br />
<br />
A celebrated result of Eisenbud--Kimshaishvili--Levine computes the local Brouwer degree of a real polynomial function at an isolated zero as the signature of a quadratic form. I will discuss a parallel result in A1-homotopy theory, and time permitting, explain how to study a singularity by applying these results to the gradient of a defining equation. This is joint work with Kirsten Wickelgren.<br />
<br />
===Vasily Dolgushev===<br />
A manifestation of the Grothendieck-Teichmueller group in geometry<br />
<br />
Inspired by Grothendieck’s lego-game, Vladimir Drinfeld introduced, in<br />
1990, the Grothendieck-Teichmueller group GRT. This group has<br />
interesting links to the absolute Galois group of rationals, moduli of<br />
algebraic curves, solutions of the Kashiwara-Vergne problem, and<br />
theory of motives. My talk will be devoted to the manifestation of GRT<br />
in the extended moduli of algebraic varieties, which was conjectured<br />
by Maxim Kontsevich in 1999. My talk is partially based on the joint<br />
paper with Chris Rogers and Thomas Willwacher: http://arxiv.org/abs/1211.4230.</div>Maxim