https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Luwang&feedformat=atomUW-Math Wiki - User contributions [en]2021-01-25T04:44:43ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15499Geometry and Topology Seminar 2019-20202018-05-04T15:51:52Z<p>Luwang: /* Fall 2018 */</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 Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|TBA<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== TBA ===<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15498Geometry and Topology Seminar 2019-20202018-05-04T15:50:46Z<p>Luwang: </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 Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2018 ==<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 />
<br />
<br />
== Fall Abstracts ==<br />
<br />
=== TBA ===<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2017-2018&diff=15497Geometry and Topology Seminar 2017-20182018-05-04T15:48:10Z<p>Luwang: Created page with "The Geometry and Topology seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''. <br> For more information, contact [http://www.ma..."</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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 1<br />
|Andre Neves (Distinguished Lecture) <br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 2<br />
|Andre Neves (Distinguished Lecture)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15496Geometry and Topology Seminar 2019-20202018-05-04T15:47:58Z<p>Luwang: /* Archive of past Geometry seminars */</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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 1<br />
|Andre Neves (Distinguished Lecture) <br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 2<br />
|Andre Neves (Distinguished Lecture)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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 />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15492Geometry and Topology Seminar 2019-20202018-05-02T22:13:16Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 1<br />
|Andre Neves (Distinguished Lecture) <br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 2<br />
|Andre Neves (Distinguished Lecture)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15491Geometry and Topology Seminar 2019-20202018-05-02T19:55:26Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 1<br />
|Andre Neves (Distinguished Lecture) <br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 2<br />
|Andre Neves (Distinguished Lecture)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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 />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15461Colloquia/Fall182018-04-24T22:54:00Z<p>Luwang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<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 />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#April 16, Christine Berkesch Zamaere (University of Minnesota)| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday, Room: 911)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Tsuda University) Wasow lecture<br />
|[[#April 25, Hitoshi Ishii (Tsuda University)| Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[#May 1, Andre Neves (University Chicago and Imperial College London)| Wow, so many minimal surfaces! (Part I)]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[#May 2, Andre Neves (University Chicago and Imperial College London)| Wow, so many minimal surfaces! (Part II) ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<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 />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16, Christine Berkesch Zamaere (University of Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
===April 25, Hitoshi Ishii (Tsuda University)===<br />
Title: Asymptotic problems for Hamilton-Jacobi equations and weak KAM theory<br />
<br />
Abstract: In the lecture, I discuss two asymptotic problems related to Hamilton-Jacobi equations. One concerns the long-time behavior of solutions of time evolutionary Hamilton-Jacobi equations and the other is the so-called vanishing discount problem for stationary Hamilton-Jacobi equations. The last two decades have seen a fundamental importance of weak KAM theory in the asymptotic analysis of Hamilton-Jacobi equations. I explain briefly the Aubry sets and Mather measures from weak KAM theory and their use in the analysis of the two asymptotic problems above.<br />
<br />
===May 1 and 2, Andre Neves (University of Chicago and Imperial College London)===<br />
Title: Wow, so many minimal surfaces!<br />
<br />
Abstract: Minimal surfaces are ubiquitous in geometry and applied science but their existence theory is rather mysterious. For instance, Yau in 1982 conjectured that any 3-manifold admits infinitely many closed minimal surfaces but the best one knows is the existence of at least three.<br />
<br />
After a brief historical account, I will talk about my ongoing work with Marques and the progress we made on this question jointly with Irie and Song: we showed that for generic metrics, minimal hypersurfaces are dense and equidistributed. In particular, this settles Yau’s conjecture for generic metrics.<br />
<br />
The first talk will be more general and the second talk will contain proofs of the denseness and equidistribution results. This part is join work with Irie, Marques, and Song.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15393Colloquia/Fall182018-04-11T15:28:30Z<p>Luwang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<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 />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13 (911 Van Vleck)<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#Berkesch| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm, Room: B102 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm, Room: B325 VV)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<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 />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16 Christine Berkesch Zamaere (Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Blank|Fall 2018]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15392Geometry and Topology Seminar 2019-20202018-04-11T14:35:43Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 1<br />
|Andre Neves (Distinguished Lecture) <br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 2<br />
|Andre Neves (Distinguished Lecture)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15378Colloquia/Fall182018-04-09T14:11:30Z<p>Luwang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<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 />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#Berkesch| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday, 4:30pm)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday, 3pm)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<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 />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16 Christine Berkesch Zamaere (Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15377Colloquia/Fall182018-04-09T13:58:15Z<p>Luwang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<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 />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[#January 29 Li Chao (Columbia)| Elliptic curves and Goldfeld's conjecture ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2 (Room: 911)<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 5 (Monday, Room: 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 6 (Tuesday 2 pm, Room 911)<br />
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University) <br />
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]<br />
| Ellenberg, Gurevitch<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[#February 9 Wes Pegden (CMU)| The fractal nature of the Abelian Sandpile ]]<br />
| Roch<br />
|<br />
|-<br />
|March 2<br />
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)<br />
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]<br />
| Caldararu<br />
|<br />
|-<br />
| March 16 (Room: 911)<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[#March 16 Anne Gelb (Dartmouth)| Reducing the effects of bad data measurements using variance based weighted joint sparsity ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 5 (Thursday, Room: 911)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[#April 5 John Baez (UC Riverside)| Monoidal categories of networks ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)<br />
|[[# Edray Goins| Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[#April 13, Jill Pipher, Brown University| Mathematical ideas in cryptography ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 16 (Monday)<br />
| [http://www-users.math.umn.edu/~cberkesc/ Christine Berkesch Zamaere ] (University of Minnesota)<br />
|[[#Berkesch| Free complexes on smooth toric varieties ]]<br />
| Erman, Sam<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
| May 1 (Tuesday)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 2 (Wednesday)<br />
| [https://math.uchicago.edu/~aneves/ Andre Neves] (University of Chicago and Imperial College London) Distinguished lecture<br />
|[[# TBA| TBA ]]<br />
| Lu Wang<br />
|<br />
|-<br />
| May 4<br />
| [http://math.mit.edu/~cohn/ Henry Cohn] (Microsoft Research and MIT)<br />
|[[# TBA| TBA ]]<br />
| Ellenberg<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 />
<br />
===January 29 Li Chao (Columbia)===<br />
<br />
Title: Elliptic curves and Goldfeld's conjecture<br />
<br />
Abstract: <br />
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.<br />
<br />
=== February 2 Thomas Fai (Harvard) ===<br />
<br />
Title: The Lubricated Immersed Boundary Method<br />
<br />
Abstract:<br />
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.<br />
<br />
===February 5 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes<br />
<br />
Abstract: <br />
<br />
Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders. <br />
<br />
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. <br />
<br />
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders. <br />
<br />
<br />
===February 6 Alex Lubotzky (Hebrew University)===<br />
<br />
Title: Groups' approximation, stability and high dimensional expanders<br />
<br />
Abstract: <br />
<br />
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.<br />
<br />
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. <br />
<br />
All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.<br />
<br />
===February 9 Wes Pegden (CMU)===<br />
<br />
Title: The fractal nature of the Abelian Sandpile <br />
<br />
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor. <br />
<br />
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation). We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings. In this talk, we will survey our work in this area, and discuss avenues of current and future research.<br />
<br />
===March 2 Aaron Bertram (Utah)===<br />
<br />
Title: Stability in Algebraic Geometry<br />
<br />
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.<br />
<br />
===March 16 Anne Gelb (Dartmouth)===<br />
<br />
Title: Reducing the effects of bad data measurements using variance based weighted joint sparsity<br />
<br />
Abstract: We introduce the variance based joint sparsity (VBJS) method for sparse signal recovery and image reconstruction from multiple measurement vectors. Joint sparsity techniques employing $\ell_{2,1}$ minimization are typically used, but the algorithm is computationally intensive and requires fine tuning of parameters. The VBJS method uses a weighted $\ell_1$ joint sparsity algorithm, where the weights depend on the pixel-wise variance. The VBJS method is accurate, robust, cost efficient and also reduces the effects of false data.<br />
<br />
<br />
<br />
<br />
===April 5 John Baez (UC Riverside)===<br />
<br />
Title: Monoidal categories of networks<br />
<br />
Abstract: Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, chemical reaction networks, signal-flow graphs, Bayesian networks, food webs, Feynman diagrams and the like. Far from mere informal tools, many of these diagrammatic languages fit into a rigorous framework: category theory. I will explain a bit of how this works and discuss some applications.<br />
<br />
<br />
<br />
<br />
<br />
===April 6 Edray Goins (Purdue)===<br />
<br />
Title: Toroidal Bely&#301; Pairs, Toroidal Graphs, and their Monodromy Groups<br />
<br />
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math> A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1. Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math> Replacing <math> \mathbb P^1 </math> with an elliptic curve <math>E </math>, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math> Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair. The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math><br />
<br />
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups. For each positive integer <math> N </math>, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math> Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N. For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph. Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math> We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus. <br />
<br />
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.<br />
<br />
===April 13, Jill Pipher, Brown University===<br />
<br />
Title: Mathematical ideas in cryptography<br />
<br />
Abstract: This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,<br />
including homomorphic encryption.<br />
<br />
===April 16 Christine Berkesch Zamaere (Minnesota)===<br />
Title: Free complexes on smooth toric varieties<br />
<br />
Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15376Geometry and Topology Seminar 2019-20202018-04-09T13:52:42Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|[[#Pei-Ken Hung|"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"]]<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<br />
<br />
===Yu Li===<br />
<br />
"The rigidity of Ricci shrinkers of dimension four"<br />
<br />
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.<br />
This is a joint work with Bing Wang.<br />
<br />
===Pei-Ken Hung===<br />
<br />
"A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold"<br />
<br />
We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the Euclidean space, and has an interpretation from general relativity. The proof relies on a monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15164Geometry and Topology Seminar 2019-20202018-02-21T01:25:12Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|Wei Ho<br />
|TBA<br />
|Daniel Erman<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15147Geometry and Topology Seminar 2019-20202018-02-18T16:43:47Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|Yuan Yuan (Syracuse)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|Wei Ho<br />
|TBA<br />
|Daniel Erman<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|Pei-Ken Hung (Columbia Univ.)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15144Geometry and Topology Seminar 2019-20202018-02-17T16:16:30Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|Yuan Yuan (Syracuse)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|Wei Ho<br />
|TBA<br />
|Daniel Erman<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14940Geometry and Topology Seminar 2019-20202018-01-31T16:24:24Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]<br />
|Local<br />
|-<br />
|February 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|Yu Li<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14857Geometry and Topology Seminar 2019-20202018-01-24T19:22:10Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|TBA<br />
|Local<br />
|-<br />
|February 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14856Geometry and Topology Seminar 2019-20202018-01-24T19:20:14Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|Jingrui Cheng<br />
|Estimates for constant scalar curvature Kahler metrics with applications to existence<br />
|Local<br />
|-<br />
|February 2<br />
|Jingrui Cheng<br />
|TBA<br />
|Local<br />
|-<br />
|February 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== Jingrui Cheng ===<br />
<br />
"Estimates for constant scalar curvature Kahler metrics with applications to existence"<br />
<br />
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14761Geometry and Topology Seminar 2019-20202018-01-12T02:58:45Z<p>Luwang: </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 />
== 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 />
|January 26<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|February 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 2<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 9<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 16<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|March 23<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b> Spring Break </b><br />
|<br />
|<br />
|-<br />
|April 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|April 27<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|May 4<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<br />
|}<br />
== Spring Abstracts ==<br />
<br />
=== TBA ===<br />
<br />
TBA<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14404Geometry and Topology Seminar 2019-20202017-10-20T14:09:46Z<p>Luwang: </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| "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 />
"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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14397Colloquia/Fall182017-10-19T20:22:11Z<p>Luwang: </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, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko 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 />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<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 />
|[[# 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 />
== 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 />
===October 13: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<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 />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14281Geometry and Topology Seminar 2019-20202017-10-02T19:08:57Z<p>Luwang: </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 />
|TBA<br />
|Max<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"Topology of closed geodesics on surfaces and curve shortening"<br />
<br />
A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.<br />
<br />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Sebastian Baader ===<br />
"A filtration of the Gordian complex via symmetric groups"<br />
<br />
The Gordian complex is a countable graph whose vertices correspond to knot types and whose edges correspond to pairs of knots that are related by a crossing change in a suitable diagram. For every natural number n, we consider the subgraph of the Gordian complex defined by restricting to the knot types whose fundamental group surjects onto S_n. We will prove that the various inclusion maps from these subgraphs into the Gordian complex are isometric embeddings. From this, we obtain a simple metric filtration of the Gordian complex.<br />
<br />
=== Shengwen Wang ===<br />
"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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14270Geometry and Topology Seminar 2019-20202017-09-28T20:15:30Z<p>Luwang: </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 />
|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 />
=== Ke Zhu===<br />
"Isometric Embedding via Heat Kernel"<br />
<br />
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.<br />
<br />
=== Shaosai Huang ===<br />
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"<br />
<br />
A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant. <br />
<br />
=== Shengwen Wang ===<br />
"TBA"<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14127Geometry and Topology Seminar 2019-20202017-09-14T00:33:52Z<p>Luwang: </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 />
|TBA<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 />
|(reserved)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"<br />
<br />
Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK<br />
metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with<br />
Jeff Viaclovsky.<br />
<br />
=== Sigurd Angenent ===<br />
"TBA"<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14085Geometry and Topology Seminar 2019-20202017-09-07T19:32:10Z<p>Luwang: </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<br />
|TBA<br />
|Local <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<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 />
|(reserved)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Jiyuan Han ===<br />
"TBA"<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 />
<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14075Geometry and Topology Seminar 2019-20202017-09-06T16:28:22Z<p>Luwang: </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<br />
|TBA<br />
|Local <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<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 />
|(reserved)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<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 />
=== Jiyuan Han ===<br />
"TBA"<br />
<br />
=== Shaosai Huang ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
=== Shengwen Wang ===<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=14050Geometry and Topology Seminar 2019-20202017-09-04T23:01:20Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|TBA<br />
|TBA<br />
|TBA <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 29<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 6<br />
|Shaosai Huang(Stony Brook)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|October 13<br />
|(reserved)<br />
|TBA<br />
|Kjuchukova<br />
|-<br />
|October 20<br />
|Shengwen Wang (Johns Hopkins)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|Ovidiu Munteanu (University of Connecticut)<br />
|TBA<br />
|Bing Wang<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
=== Shaosai Huang ===<br />
"TBA"<br />
<br />
=== Ovidiu Munteanu ===<br />
"TBA"<br />
<br />
=== Shengwen Wang ===<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13816Geometry and Topology Seminar 2019-20202017-07-12T00:51:05Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|TBA<br />
|TBA<br />
|TBA <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 29<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 27<br />
|Marco Mendez-Guaraco (Chicago)<br />
|TBA<br />
|Lu Wang<br />
|-<br />
|November 3<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 10<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|November 17<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Marco Mendez-Guaraco ===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13795Geometry and Topology Seminar 2019-20202017-06-23T20:37:05Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
== Fall 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 15<br />
|TBA<br />
|TBA<br />
|TBA <br />
|-<br />
|September 22<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|September 29<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 6<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 13<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 20<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|October 27<br />
|TBA<br />
|TBA<br />
|TBA<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 />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|<b>Thanksgiving Recess</b><br />
| <br />
| <br />
| <br />
|-<br />
|December 1<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|December 8<br />
|TBA<br />
|TBA<br />
|TBA<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== 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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2016-2017&diff=13794Geometry and Topology Seminar 2016-20172017-06-23T20:20:32Z<p>Luwang: </p>
<hr />
<div>== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "The Anomaly Flow and Strominger systems"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
|[[#Paul Feehan| "The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "A Frobenius-Nirenberg theorem with parameter"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"Random walks on groups with negative curvature"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "Obstructions to Nielsen realization"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Paul Feehan===<br />
"The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"<br />
<br />
The Lojasiewicz-Simon gradient inequality is a generalization, due to Leon Simon (1983), to analytic or Morse-Bott functionals on Banach manifolds of the finite-dimensional gradient inequality, due to Stanislaw Lojasiewicz (1963), for analytic functions on Euclidean space. We shall discuss several recent generalizations of the Lojasiewicz-Simon gradient inequality and a selection of their applications, such as global existence and convergence of Yang-Mills gradient flow over four-dimensional manifolds and discreteness of the energy spectrum for harmonic maps from Riemann surfaces into analytic Riemannian manifolds.<br />
<br />
===Xianghong Gong===<br />
"A Frobenius-Nirenberg theorem with parameter"<br />
<br />
The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the complex structure in the complex Euclidean space. We will show two results about the Newlander-Nirenberg theorem with parameter. The first extends the Newlander-Nirenberg theorem to a parametric version, and its proof yields a sharp regularity result as Webster's proof for the Newlander-Nirenberg theorem. The second concerns a version of Nirenberg's complex Frobenius theorem and its proof yields a result with a mild loss of regularity.<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Joseph Maher===<br />
"Random walks on groups with negative curvature"<br />
<br />
We will give an introduction to random walks on groups satisfying various types of negative curvature conditions. A simple example is the nearest neighbour random walk on the 4-valent tree, also known as the Cayley graph of the free group on two generators. A typical random walk moves away from the origin at linear speed, and converges to one of the ends of the tree. We will discuss how to generalize this result to more general settings, such as hyperbolic groups, or acylindrical groups. This is joint work with Giulio Tiozzo.<br />
<br />
===Bena Tshishiku===<br />
"Obstructions to Nielsen realization"<br />
<br />
Let M be a manifold, and let Mod(M) be the group of diffeomorphisms of M modulo isotopy (the mapping class group). The Nielsen realization problem for diffeomorphisms asks, “Can a given subgroup G<Mod(M) be lifted to the diffeomorphism group Diff(M)?” This question about group actions is related to a question about flat connections on fiber bundles with fiber M. In the case M is a closed surface, the answer is “yes" for finite G (by work of Kerckhoff) and “no" for G=Mod(M) (by work of Morita). For most infinite G<Mod(M), we don't know. I will discuss some obstructions that can be used to show that certain groups don’t lift. Some of this work is joint with Nick Salter. <br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"The Anomaly Flow and Strominger systems"<br />
<br />
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and S. Picard.<br />
<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 />
== 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.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13617Geometry and Topology Seminar 2019-20202017-04-04T19:44:49Z<p>Luwang: </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 />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "The Anomaly Flow and Strominger systems"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
|[[#Paul Feehan| "The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "A Frobenius-Nirenberg theorem with parameter"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Paul Feehan===<br />
"The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"<br />
<br />
The Lojasiewicz-Simon gradient inequality is a generalization, due to Leon Simon (1983), to analytic or Morse-Bott functionals on Banach manifolds of the finite-dimensional gradient inequality, due to Stanislaw Lojasiewicz (1963), for analytic functions on Euclidean space. We shall discuss several recent generalizations of the Lojasiewicz-Simon gradient inequality and a selection of their applications, such as global existence and convergence of Yang-Mills gradient flow over four-dimensional manifolds and discreteness of the energy spectrum for harmonic maps from Riemann surfaces into analytic Riemannian manifolds.<br />
<br />
===Xianghong Gong===<br />
"A Frobenius-Nirenberg theorem with parameter"<br />
<br />
The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the complex structure in the complex Euclidean space. We will show two results about the Newlander-Nirenberg theorem with parameter. The first extends the Newlander-Nirenberg theorem to a parametric version, and its proof yields a sharp regularity result as Webster's proof for the Newlander-Nirenberg theorem. The second concerns a version of Nirenberg's complex Frobenius theorem and its proof yields a result with a mild loss of regularity.<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"The Anomaly Flow and Strominger systems"<br />
<br />
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and S. Picard.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13571Geometry and Topology Seminar 2019-20202017-03-28T03:41:45Z<p>Luwang: </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 />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "The Anomaly Flow and Strominger systems"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
|[[#Paul Feehan| "The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Paul Feehan===<br />
"The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory"<br />
<br />
The Lojasiewicz-Simon gradient inequality is a generalization, due to Leon Simon (1983), to analytic or Morse-Bott functionals on Banach manifolds of the finite-dimensional gradient inequality, due to Stanislaw Lojasiewicz (1963), for analytic functions on Euclidean space. We shall discuss several recent generalizations of the Lojasiewicz-Simon gradient inequality and a selection of their applications, such as global existence and convergence of Yang-Mills gradient flow over four-dimensional manifolds and discreteness of the energy spectrum for harmonic maps from Riemann surfaces into analytic Riemannian manifolds.<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"The Anomaly Flow and Strominger systems"<br />
<br />
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and S. Picard.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13520Geometry and Topology Seminar 2019-20202017-03-17T19:40:59Z<p>Luwang: </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 />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "The Anomaly Flow and Strominger systems"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
|[[#Paul Feehan| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Paul Feehan===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"The Anomaly Flow and Strominger systems"<br />
<br />
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and S. Picard.<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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13487PDE Geometric Analysis seminar2017-03-09T04:25:52Z<p>Luwang: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Mean-Field Limits for Ginzburg-Landau vortices ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Microscopic description of Coulomb-type systems ]]<br />
| <br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | Analysis of Velázquez's solution to the mean curvature flow with a type II singularity]]<br />
| Lu Wang<br />
<br />
<br />
|-<br />
|April 24<br />
| Jianfeng Lu<br />
|[[#Jianfeng Lu | TBA]]<br />
| Li<br />
<br />
|-<br />
|April 25- joint Analysis/PDE seminar<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
===Eric Baer===<br />
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.<br />
<br />
===Ben Seeger===<br />
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.<br />
<br />
===Sylvia Serfaty===<br />
Mean-Field Limits for Ginzburg-Landau vortices<br />
<br />
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.<br />
<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.<br />
<br />
===Siao-hao Guo===<br />
Analysis of Velázquez's solution to the mean curvature flow with a type II singularity<br />
<br />
Velázquez discovered a solution to the mean curvature flow which develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution, the rescaled flow converges in the C^0 sense to a minimal hypersurface which is tangent to Simons' cone at infinity. In this talk, we will present that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we will show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form. This is a joint work with N. Sesum.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13486PDE Geometric Analysis seminar2017-03-09T04:25:07Z<p>Luwang: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Mean-Field Limits for Ginzburg-Landau vortices ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | Microscopic description of Coulomb-type systems ]]<br />
| <br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | Analysis of Velázquez's solution to the mean curvature flow with a type II singularity]]<br />
| Lu Wang<br />
<br />
<br />
|-<br />
|April 24<br />
| Jianfeng Lu<br />
|[[#Jianfeng Lu | TBA]]<br />
| Li<br />
<br />
|-<br />
|April 25- joint Analysis/PDE seminar<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
===Eric Baer===<br />
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.<br />
<br />
===Ben Seeger===<br />
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.<br />
<br />
===Sylvia Serfaty===<br />
Mean-Field Limits for Ginzburg-Landau vortices<br />
<br />
Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. This talk will review some results on the derivation of effective models to describe the statics and dynamics of these vortices, with particular attention to the situation where the number of vortices blows up with the parameters of the problem. In particular we will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (=Schrodinger Ginzburg-Landau) equation.<br />
<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.<br />
<br />
==Siao-hao Guo===<br />
Analysis of Velázquez's solution to the mean curvature flow with a type II singularity<br />
<br />
Velázquez discovered a solution to the mean curvature flow which develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution, the rescaled flow converges in the C^0 sense to a minimal hypersurface which is tangent to Simons' cone at infinity. In this talk, we will present that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we will show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form. This is a joint work with N. Sesum.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13448PDE Geometric Analysis seminar2017-03-04T19:50:56Z<p>Luwang: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|[[#Eric Baer | Isoperimetric sets inside almost-convex cones]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | Homogenization of pathwise Hamilton-Jacobi equations ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| <br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | TBA]]<br />
| Lu Wang<br />
<br />
<br />
|-<br />
|April 24<br />
| Jianfeng Lu<br />
|[[#Jianfeng Lu | TBA]]<br />
| Li<br />
<br />
|-<br />
|April 25- joint Analysis/PDE seminar<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
===Eric Baer===<br />
We discuss a recent result showing that a characterization of isoperimetric sets (that is, sets minimizing a relative perimeter functional with respect to a fixed volume constraint) inside convex cones as sections of balls centered at the origin (originally due to P.L. Lions and F. Pacella) remains valid for a class of "almost-convex" cones. Key tools include compactness arguments and the use of classically known sharp characterizations of lower bounds for the first nonzero Neumann eigenvalue associated to (geodesically) convex domains in the hemisphere. The work we describe is joint with A. Figalli.<br />
<br />
===Ben Seeger===<br />
I present a homogenization result for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. In doing so, I derive a new well-posedness result when the Hamiltonian is smooth, convex, and positively homogenous. I also demonstrate that equations involving multiple driving signals may homogenize or exhibit blow-up.<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13400Geometry and Topology Seminar 2019-20202017-02-20T13:49:32Z<p>Luwang: </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 />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| [https://www.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
|[[#Paul Feehan| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Paul Feehan===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=13367PDE Geometric Analysis seminar2017-02-16T03:35:41Z<p>Luwang: </p>
<hr />
<div>The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
===[[Fall 2016 | Tentative schedule for Fall 2017]]===<br />
<br />
= PDE GA Seminar Schedule Spring 2017 =<br />
<br />
{| cellpadding="8"<br />
!style="width:20%" align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!style="width:20%" align="left" | host(s)<br />
|-<br />
|January 23<br>Special time and location:<br> 3-3:50pm, B325 Van Vleck<br />
| Sigurd Angenent (UW)<br />
|[[#Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|January 30<br />
| Serguei Denissov (UW)<br />
|[[#Serguei Denissov | Instability in 2D Euler equation of incompressible inviscid fluid]]<br />
| Kim & Tran<br />
|- <br />
<br />
<br />
|-<br />
|February 6 - Wasow lecture<br />
| Benoit Perthame (University of Paris VI)<br />
|[[#| ]]<br />
| Jin<br />
|- <br />
<br />
<br />
|-<br />
|February 13<br />
| Bing Wang (UW)<br />
|[[#Bing Wang | The extension problem of the mean curvature flow]]<br />
| Kim & Tran<br />
|- <br />
<br />
|-<br />
|February 20<br />
| Eric Baer (UW)<br />
|<br />
| <br />
|- <br />
<br />
|-<br />
|February 27<br />
| Ben Seeger (University of Chicago)<br />
|[[#Ben Seeger | ]]<br />
| Tran<br />
|- <br />
<br />
|-<br />
|March 7 - Mathematics Department Distinguished Lecture<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | On the mathematical modeling of the humid atmosphere]]<br />
| Smith <br />
|- <br />
<br />
<br />
|-<br />
|March 8 - Analysis/Applied math/PDE seminar<br />
| Roger Temam (Indiana University) <br />
|[[#Roger Temam | Weak solutions of the Shigesada-Kawasaki-Teramoto system ]]<br />
| Smith<br />
|-<br />
<br />
|-<br />
|March 13<br />
| Sona Akopian (UT-Austin)<br />
|[[#Sona Akopian | ]]<br />
| Kim<br />
<br />
|-<br />
|March 27 - Analysis/PDE seminar<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| Tran<br />
<br />
|-<br />
|March 29 - Wasow lecture<br />
| Sylvia Serfaty (Courant)<br />
|[[#Sylvia Serfaty | ]]<br />
| <br />
<br />
|-<br />
|April 3<br />
| Zhenfu Wang (Maryland)<br />
|[[#Zhenfu Wang | ]]<br />
| Kim<br />
<br />
|-<br />
|April 10<br />
| Andrei Tarfulea (Chicago)<br />
|[[#Andrei Tarfulea | Improved estimates for thermal fluid equations]]<br />
| Baer<br />
<br />
|-<br />
|April 17<br />
| Siao-Hao Guo (Rutgers)<br />
|[[# Siao-Hao Guo | ]]<br />
| Lu Wang<br />
<br />
|-<br />
|April 24<br />
| Chris Henderson (Chicago)<br />
|[[#Chris Henderson | TBA]]<br />
| Lin<br />
<br />
|-<br />
|May 1st<br />
| Jeffrey Streets (UC-Irvine)<br />
|[[#Jeffrey Streets | ]]<br />
| Bing Wang<br />
|}<br />
<br />
=Abstracts=<br />
<br />
===Sigurd Angenent===<br />
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so. Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient Solutions.&rdquo; In doing so one finds that there is interesting dynamics associated to ancient solutions. I will discuss what is currently known about these solutions. Some of the talk is based on joint work with Sesum and Daskalopoulos.<br />
<br />
===Serguei Denissov===<br />
We consider the patch evolution under the 2D Euler dynamics and study how the geometry of the boundary can deteriorate in time.<br />
<br />
<br />
===Bing Wang===<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R3. This is a joint work with H.Z. Li.<br />
<br />
<br />
===Andrei Tarfulea===<br />
We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and<br />
dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13336Geometry and Topology Seminar 2019-20202017-02-10T19:43:17Z<p>Luwang: </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 />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "Free boundary minimal hypersurfaces of Euclidean domains"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "Stable classification of 4-manifolds"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"Free boundary minimal hypersurfaces of Euclidean domains"<br />
<br />
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Mark Powell===<br />
''Stable classification of 4-manifolds''<br />
<br />
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. <br />
Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations.<br />
Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. <br />
As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
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>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13152Geometry and Topology Seminar 2019-20202017-01-28T04:14:24Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13151Geometry and Topology Seminar 2019-20202017-01-28T04:13:48Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13150Geometry and Topology Seminar 2019-20202017-01-28T04:13:08Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "Metrics of positive scalar curvature and unbounded min-max widths"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Paul Feehan===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"Metrics of positive scalar curvature and unbounded min-max widths"<br />
<br />
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13134Geometry and Topology Seminar 2019-20202017-01-26T14:00:42Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| reserved <br />
|<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Paul Feehan===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"TBA"<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13133Geometry and Topology Seminar 2019-20202017-01-26T13:59:14Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "Intersectional Invariant Random Subgroups and Furstenberg Entropy."]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| Paul Feehan (Rutgers) <br />
| [[#Paul Feehan| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Paul Feehan===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"TBA"<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Yair Hartman===<br />
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."<br />
<br />
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.<br />
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13099Geometry and Topology Seminar 2019-20202017-01-23T13:07:14Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| [https://www.math.wisc.edu/~gong/ Xianghong Gong] (Wisconsin) <br />
| [[#Xianghong Gong| "TBA"]]<br />
| local<br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"TBA"<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13037Geometry and Topology Seminar 2019-20202017-01-18T19:40:51Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| Rafael Montezuma (University of Chicago) <br />
| [[#Rafael Montezuma| "TBA"]]<br />
| Lu Wang<br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| <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 />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Rafael Montezuma===<br />
"TBA"<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=13003Geometry and Topology Seminar 2019-20202017-01-16T17:30:21Z<p>Luwang: </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 />
| [http://math.uchicago.edu/~lambrozio/ Lucas Ambrozio] (University of Chicago)<br />
| [[#Lucas Ambrozio| "TBA"]] <br />
| Lu Wang <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| <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 />
===Lucas Ambrozio===<br />
"TBA"<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12980Geometry and Topology Seminar 2019-20202017-01-14T15:26:26Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| Reserved<br />
| <br />
| Kjuchukova<br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| Lu Wang<br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12979Geometry and Topology Seminar 2019-20202017-01-14T15:19:30Z<p>Luwang: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| Reserved<br />
| <br />
| Kjuchukova<br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| [http://www.math.uci.edu/~xiangwen/ Xiangwen Zhang] (University of California-Irvine)<br />
| [[#Xiangwen Zhang| "TBA"]]<br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
===Xiangwen Zhang===<br />
"TBA"<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Luwanghttps://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12816Geometry and Topology Seminar 2019-20202016-12-09T19:14:40Z<p>Luwang: </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| "TBA"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| <br />
| <br />
| <br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
| <br />
| <br />
| <br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== 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>Luwang