https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Shuang78&feedformat=atomUW-Math Wiki - User contributions [en]2020-08-09T12:16:04ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=19456Geometry and Topology Seminar2020-07-23T16:37:51Z<p>Shuang78: </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 />
[[Geometry_and_Topology_Seminar_2020-2021]]<br />
<br />
== Fall 2020 ==<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 />
|Max Hallgren (Cornell)<br />
| TBA<br />
|(Huang)<br />
|-<br />
|TBA<br />
|Yi Lai (Berkeley)<br />
| TBA<br />
|(Huang)<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]<br />
<br><br><br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19450Geometry and Topology Seminar 2019-20202020-07-22T18:24:24Z<p>Shuang78: Shuang78 moved page Geometry and Topology Seminar to Geometry and Topology Seminar 2019-2020: As we have finished the academic year 2019-2020 and we are entering a new academic year, we will need a new link to the G&T 2020-2021 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 Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar&diff=19451Geometry and Topology Seminar2020-07-22T18:24:24Z<p>Shuang78: Shuang78 moved page Geometry and Topology Seminar to Geometry and Topology Seminar 2019-2020: As we have finished the academic year 2019-2020 and we are entering a new academic year, we will need a new link to the G&T 2020-2021 seminars.</p>
<hr />
<div>#REDIRECT [[Geometry and Topology Seminar 2019-2020]]</div>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19449Geometry and Topology Seminar 2019-20202020-07-22T18:16:17Z<p>Shuang78: </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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19448Geometry and Topology Seminar 2019-20202020-07-22T18:15:54Z<p>Shuang78: </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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19447Geometry and Topology Seminar 2019-20202020-07-22T18:15:41Z<p>Shuang78: </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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19446Geometry and Topology Seminar 2019-20202020-07-22T18:15:19Z<p>Shuang78: </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 />
== Fall 2020 ==<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 />
|Max Hallgren (Cornell)<br />
|TBA<br />
<br />
|(Huang)<br />
|-<br />
|TBA<br />
|Yi Lai (Berkeley)<br />
|TBA<br />
<br />
|(Huang)<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19445Geometry and Topology Seminar 2019-20202020-07-22T18:14:12Z<p>Shuang78: </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 />
== Fall 2020 ==<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 />
|Max Hallgren (Cornell)<br />
|TBA<br />
<br />
|(Huang)<br />
|-<br />
|TBA<br />
|Yi Lai (Berkeley)<br />
|TBA<br />
<br />
|(Huang)<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=19444Geometry and Topology Seminar 2019-20202020-07-22T18:13:26Z<p>Shuang78: </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 />
== Fall 2020 ==<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 />
|Max Hallgren (Cornell)<br />
|TBA<br />
|(Huang)<br />
|-<br />
|TBA<br />
|Yi Lai (Berkeley)<br />
|TBA<br />
|(Huang)<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3: Quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces<br />
<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|-<br />
|Mar. 13 <b>CANCELED</b> <br />
|Karin Melnick (University of Maryland)<br />
|A D'Ambra Theorem in conformal Lorentzian geometry<br />
|(Dymarz)<br />
|-<br />
|<b>Mar. 25</b> <b>CANCELED</b><br />
|Joerg Schuermann (University of Muenster, Germany)<br />
|An introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles<br />
|(Maxim)<br />
|-<br />
|Mar. 27 <b>CANCELED</b><br />
|David Massey (Northeastern University)<br />
|Extracting easily calculable algebraic data from the vanishing cycle complex<br />
|(Maxim)<br />
|-<br />
|Apr. 10<br />
|Antoine Song (Berkeley)<br />
|TBA<br />
|(Chen)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Xiangdong Xie===<br />
<br />
The quasiconformal structure on the ideal boundary of Gromov hyperbolic spaces has played<br />
an important role in various rigidity questions in geometry and group theory.<br />
In these talks I shall give an introduction to this topic. In the first talk I will introduce Gromov hyperbolic spaces, define their ideal boundary, and discuss their basic properties. In the second and third talks I will define the visual metrics on the ideal boundary, explain the connection between quasiisometries of Gromov hyperbolic space and quasiconformal maps on their ideal boundary, and indicate how the quasiconformal structure on the ideal boundary can be used to deduce rigidity.<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
===Karin Melnick===<br />
<br />
D'Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.<br />
<br />
===Joerg Schuermann===<br />
<br />
We give an introduction to Poincare-Hopf theorems for singular spaces via characteristic cycles, based on stratified Morse theory for constructible functions. The corresponding local index of an isolated critical point (in a stratified sense) of a one-form depends on the constructible function, specializing for different choices to well known indices like the radial, GSV or Euler obstruction index.<br />
<br />
===David Massey===<br />
<br />
Given a complex analytic function on an open subset U of C<sup>n+1</sup>, one may consider the complex of sheaves of vanishing cycles along f of the constant sheaf Z<sub>U</sub>. This complex encodes on the cohomological level the reduced cohomology of the Milnor fibers of f at each of f<sup>-1</sup>(0). The question is: how does one calculate (ideally, by hand) any useful numbers about this vanishing cycle complex? One answer is to look at the Lê numbers of f. We will discuss the precise relationship between these objects/numbers.<br />
<br />
===Antoine Song===<br />
<br />
TBA<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18865Colloquia2020-02-02T06:23:11Z<p>Shuang78: /* Spring 2020 */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|Joe Kileel (Princeton)<br />
|[[TBA]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18731Geometry and Topology Seminar 2019-20202020-01-22T03:38:21Z<p>Shuang78: /* Spring Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
===Yuanqi Wang===<br />
$G_{2}-$instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_{2}-$instantons, with virtual dimension $0$, is expected to have interesting geometric structure and yield enumerative invariant for the underlying $7-$dimensional manifold. <br />
<br />
In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_{2}-$instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18730Geometry and Topology Seminar 2019-20202020-01-22T03:36:13Z<p>Shuang78: /* Spring 2020 */</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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|-<br />
|Mar. 6<br />
|Yuanqi Wang (University of Kansas)<br />
|Moduli space of G2−instantons on 7−dimensional product manifolds<br />
|(Huang)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18582Geometry and Topology Seminar 2019-20202019-12-29T05:41:59Z<p>Shuang78: </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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Kuang-Ru Wu===<br />
<br />
Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce Griffiths extremal Finsler metrics. As we point out, this notion is closely related to the theory of interpolation of norms, and is characterized by an equation of complex Monge– Ampere type, whose corresponding Dirichlet problem we solve. As applications, we prove that Griffiths extremal Finsler metrics quantize solutions to a natural PDE in Kahler geometry, related to the construction of flat maps for the Mabuchi metric. This is joint work with Tamas Darvas.<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18581Geometry and Topology Seminar 2019-20202019-12-29T05:39:28Z<p>Shuang78: </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 />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
|Kuang-Ru Wu (Purdue University)<br />
|Griffiths extremality, interpolation of norms, and Kahler quantization<br />
|(Huang)<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17800Colloquia2019-09-10T00:34:31Z<p>Shuang78: /* Spring 2020 */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
| Omer Mermelstein (Madison)<br />
|<br />
|Andrews<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17742Geometry and Topology Seminar 2019-20202019-09-04T18:30:11Z<p>Shuang78: /* Fall Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| TBA<br />
|(Dymarz)<br />
|-<br />
|Nov. 7<br />
|Max Forester (University of Oklahoma)<br />
| TBA<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Emily Stark===<br />
<br />
"TBA"<br />
<br />
===Max Forester===<br />
<br />
“TBA”<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17741Geometry and Topology Seminar 2019-20202019-09-04T18:29:25Z<p>Shuang78: /* Fall 2019 */</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 />
<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| TBA<br />
|(Dymarz)<br />
|-<br />
|Nov. 7<br />
|Max Forester (University of Oklahoma)<br />
| TBA<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Emily Stark===<br />
<br />
"TBA"<br />
<br />
===Max Forester===<br />
<br />
“TBA”<br />
<br />
== Archive of past Geometry seminars ==<br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17332Geometry and Topology Seminar 2019-20202019-04-17T18:34:08Z<p>Shuang78: /* Spring Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2019 ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|April 5<br />
|Mark Pengitore (Ohio)<br />
|Translation-like actions on nilpotent groups<br />
<br />
|(Dymarz)<br />
|-<br />
|April 18<br />
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)<br />
|Even Artin Groups, cohomological computations and other geometrical properties.<br />
<br />
|(Maxim)<br />
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''<br />
|-<br />
<br />
|April 19<br />
|Yan Xu (University of Missouri - St. Louis)<br />
|Structure of minimal two-spheres of constant curvature in hyperquadrics<br />
|(Huang)<br />
<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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|Quasi-isometric rigidity of a class of right angled Coxeter groups<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
<br />
==Spring Abstracts==<br />
<br />
===Mark Pengitore===<br />
<br />
"Translation-like actions on nilpotent groups"<br />
<br />
Translation-like actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is non-amenable if and only if it admits a translation-like action by a non-abelian free group. This result motivates us to ask what groups admit translation-like actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translation-like on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translation-like on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translation-like action of these two groups on each other.<br />
<br />
===José Ignacio Cogolludo Agustín===<br />
<br />
"Even Artin Groups, cohomological computations and other geometrical <br />
properties."<br />
<br />
The purpose of this talk is to introduce even Artin groups and consider<br />
their quasi-projectivity properties, as well as study the cohomological <br />
properties of their kernels, that is, the kernels of their characters.<br />
<br />
===Yan Xu===<br />
"Structure of minimal two-spheres of constant curvature in hyperquadrics"<br />
<br />
Veronese two-sphere (also called rational normal curve) is an interesting projective variety in geometry. It is of constant curvature and unique up to action of unitary group. Based on this rigidity result and SVD (singular value decomposition) in linear algebra, we give a classification of a special class minimal, especially holomorphic, two-spheres of constant curvature in hyperquadric, up to action of real orthogonal group and reparameterization of the two-sphere. For degree less than or equal to three, we give an algorithm and explicit examples. As an application of this results, by computing the norm squared of second fundamental form, we show the generic two-spheres constructed here are not homogeneous. This is a joint work with Professor Quo-Shin Chi and Zhenxiao Xie.<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.<br />
<br />
===Xiangdong Xie===<br />
"Quasi-isometric rigidity of a class of right angled Coxeter groups"<br />
<br />
Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined <br />
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).<br />
The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasi-isometry. This is joint work with Jordan Bounds.<br />
<br />
== Spring Abstracts ==<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17331Geometry and Topology Seminar 2019-20202019-04-17T18:33:49Z<p>Shuang78: /* Spring Abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2019 ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|April 5<br />
|Mark Pengitore (Ohio)<br />
|Translation-like actions on nilpotent groups<br />
<br />
|(Dymarz)<br />
|-<br />
|April 18<br />
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)<br />
|Even Artin Groups, cohomological computations and other geometrical properties.<br />
<br />
|(Maxim)<br />
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''<br />
|-<br />
<br />
|April 19<br />
|Yan Xu (University of Missouri - St. Louis)<br />
|Structure of minimal two-spheres of constant curvature in hyperquadrics<br />
|(Huang)<br />
<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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|Quasi-isometric rigidity of a class of right angled Coxeter groups<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
<br />
==Spring Abstracts==<br />
<br />
===Mark Pengitore===<br />
<br />
"Translation-like actions on nilpotent groups"<br />
<br />
Translation-like actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is non-amenable if and only if it admits a translation-like action by a non-abelian free group. This result motivates us to ask what groups admit translation-like actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translation-like on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translation-like on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translation-like action of these two groups on each other.<br />
<br />
===José Ignacio Cogolludo Agustín===<br />
<br />
"Even Artin Groups, cohomological computations and other geometrical <br />
properties."<br />
<br />
The purpose of this talk is to introduce even Artin groups and consider<br />
their quasi-projectivity properties, as well as study the cohomological <br />
properties of their kernels, that is, the kernels of their characters.<br />
<br />
<br />
===Yan Xu===<br />
"Structure of minimal two-spheres of constant curvature in hyperquadrics"<br />
<br />
Veronese two-sphere (also called rational normal curve) is an interesting projective variety in geometry. It is of constant curvature and unique up to action of unitary group. Based on this rigidity result and SVD (singular value decomposition) in linear algebra, we give a classification of a special class minimal, especially holomorphic, two-spheres of constant curvature in hyperquadric, up to action of real orthogonal group and reparameterization of the two-sphere. For degree less than or equal to three, we give an algorithm and explicit examples. As an application of this results, by computing the norm squared of second fundamental form, we show the generic two-spheres constructed here are not homogeneous. This is a joint work with Professor Quo-Shin Chi and Zhenxiao Xie.<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.<br />
<br />
===Xiangdong Xie===<br />
"Quasi-isometric rigidity of a class of right angled Coxeter groups"<br />
<br />
Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined <br />
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).<br />
The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasi-isometry. This is joint work with Jordan Bounds.<br />
<br />
== Spring Abstracts ==<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17330Geometry and Topology Seminar 2019-20202019-04-17T18:31:59Z<p>Shuang78: /* Spring 2019 */</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 />
== Spring 2019 ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|April 5<br />
|Mark Pengitore (Ohio)<br />
|Translation-like actions on nilpotent groups<br />
<br />
|(Dymarz)<br />
|-<br />
|April 18<br />
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)<br />
|Even Artin Groups, cohomological computations and other geometrical properties.<br />
<br />
|(Maxim)<br />
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''<br />
|-<br />
<br />
|April 19<br />
|Yan Xu (University of Missouri - St. Louis)<br />
|Structure of minimal two-spheres of constant curvature in hyperquadrics<br />
|(Huang)<br />
<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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|Quasi-isometric rigidity of a class of right angled Coxeter groups<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
<br />
==Spring Abstracts==<br />
<br />
===Mark Pengitore===<br />
<br />
"Translation-like actions on nilpotent groups"<br />
<br />
Translation-like actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is non-amenable if and only if it admits a translation-like action by a non-abelian free group. This result motivates us to ask what groups admit translation-like actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translation-like on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translation-like on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translation-like action of these two groups on each other.<br />
<br />
===José Ignacio Cogolludo Agustín===<br />
<br />
"Even Artin Groups, cohomological computations and other geometrical <br />
properties."<br />
<br />
The purpose of this talk is to introduce even Artin groups and consider<br />
their quasi-projectivity properties, as well as study the cohomological <br />
properties of their kernels, that is, the kernels of their characters.<br />
<br />
<br />
<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.<br />
<br />
===Xiangdong Xie===<br />
"Quasi-isometric rigidity of a class of right angled Coxeter groups"<br />
<br />
Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined <br />
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).<br />
The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasi-isometry. This is joint work with Jordan Bounds.<br />
<br />
== Spring Abstracts ==<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=17329Geometry and Topology Seminar 2019-20202019-04-17T18:31:36Z<p>Shuang78: /* Spring 2019 */</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 />
== Spring 2019 ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|April 5<br />
|Mark Pengitore (Ohio)<br />
|Translation-like actions on nilpotent groups<br />
<br />
|(Dymarz)<br />
|-<br />
|April 18<br />
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)<br />
|Even Artin Groups, cohomological computations and other geometrical properties.<br />
<br />
|(Maxim)<br />
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''<br />
|-<br />
<br />
|April 19<br />
|Yan Xu (University of Missouri - St. Louis)<br />
|Structure of minimal two-spheres of constant curvature in hyperquadrics<br />
<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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|Quasi-isometric rigidity of a class of right angled Coxeter groups<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
<br />
==Spring Abstracts==<br />
<br />
===Mark Pengitore===<br />
<br />
"Translation-like actions on nilpotent groups"<br />
<br />
Translation-like actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is non-amenable if and only if it admits a translation-like action by a non-abelian free group. This result motivates us to ask what groups admit translation-like actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translation-like on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translation-like on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translation-like action of these two groups on each other.<br />
<br />
===José Ignacio Cogolludo Agustín===<br />
<br />
"Even Artin Groups, cohomological computations and other geometrical <br />
properties."<br />
<br />
The purpose of this talk is to introduce even Artin groups and consider<br />
their quasi-projectivity properties, as well as study the cohomological <br />
properties of their kernels, that is, the kernels of their characters.<br />
<br />
<br />
<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.<br />
<br />
===Xiangdong Xie===<br />
"Quasi-isometric rigidity of a class of right angled Coxeter groups"<br />
<br />
Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined <br />
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).<br />
The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasi-isometry. This is joint work with Jordan Bounds.<br />
<br />
== Spring Abstracts ==<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16162Geometry and Topology Seminar 2019-20202018-10-08T13:16:26Z<p>Shuang78: </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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16161Geometry and Topology Seminar 2019-20202018-10-08T02:58:05Z<p>Shuang78: </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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Dingxin Zhang===<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16088Geometry and Topology Seminar 2019-20202018-09-29T17:18:47Z<p>Shuang78: </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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|TBA<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16087Geometry and Topology Seminar 2019-20202018-09-29T17:17:54Z<p>Shuang78: </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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard)<br />
|TBA<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<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>Shuang78https://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16083Geometry and Topology Seminar 2019-20202018-09-28T17:43:58Z<p>Shuang78: </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 />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<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>Shuang78