Difference between revisions of "Geometry and Topology Seminar"

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The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
 
The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
 
<br>  
 
<br>  
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .
+
For more information, contact Shaosai Huang.
  
 
[[Image:Hawk.jpg|thumb|300px]]
 
[[Image:Hawk.jpg|thumb|300px]]
  
== Fall 2016 ==
 
  
 +
== Spring 2019 ==
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date
 
!align="left" | date
Line 13: Line 13:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 9
+
|April  5
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)
+
|Mark Pengitore (Ohio)
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]
+
|Translation-like actions on nilpotent groups
| (Local)
+
 
 +
|(Dymarz)
 
|-
 
|-
|September 16
+
|April  18
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)
+
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]
+
|Even Artin Groups, cohomological computations and other geometrical properties.
| Lu Wang
+
 
 +
|(Maxim)
 +
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''
 
|-
 
|-
|September 23
+
 
| Jiyuan Han (UW Madison)
+
|April 19
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]
+
|Yan Xu (University of Missouri - St. Louis)
| (Local)
+
|Structure of minimal two-spheres of constant curvature in hyperquadrics
|-
+
|(Huang)
|September 30
+
 
|
 
|
 
|
 
|-
 
|October 7
 
| Yu Li (UW Madison) 
 
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]
 
| (Local)
 
|-
 
|October 14
 
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)
 
| [[#Sean Howe| "Representation stability and hypersurface sections"]]
 
| Melanie Matchett Wood
 
|-
 
|October 21
 
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) 
 
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]
 
| Lu Wang
 
|-
 
|October 28
 
| Ronan Conlon(Florida International University)
 
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]
 
| Bing Wang
 
|-
 
|November 4
 
| Jonathan Zhu (Harvard University)
 
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]
 
| Lu Wang
 
|-
 
|November 11
 
| [http://www.math.wisc.edu/~rkent Richard Kent] (Wisconsin)
 
| [[#Richard Kent| ''Analytic functions from hyperbolic manifolds'']]
 
| local
 
|-
 
|November 18
 
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)
 
| [[#Caglar Uyanik| "TBA"]]
 
| [http://www.math.wisc.edu/~rkent Kent]
 
|-
 
| Thanksgiving Recess
 
|
 
|
 
|
 
|-
 
|December 2
 
|Peyman Morteza (UW Madison)
 
| [[#Peyman Morteza| "TBA"]]
 
| (Local) 
 
|-
 
|December 9
 
| Yu Zeng(University of Rochester)
 
|  [[#Yu Zeng| "TBA"]]
 
|
 
|
 
|-
 
|December 16
 
|
 
|
 
|-
 
|
 
 
|}
 
|}
  
== Spring 2017 ==
+
== Fall 2018 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 99: Line 42:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Jan 20
+
|Sept. 14
+
|Teddy Einstein (UIC)
|
+
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes
|
+
|(Dymarz)
|-
 
|Jan 27
 
 
|
 
|
 
|-
 
|Feb 3
 
 
|
 
|
 
|-
 
|Feb 10
 
 
|
 
|  
 
|-
 
|Feb 17
 
 
|
 
|
 
|-
 
|Feb 24
 
 
|
 
|
 
|-
 
|March 3
 
 
|
 
|
 
|-
 
|March 10
 
 
|
 
|
 
|-
 
|March 17
 
 
|
 
|
 
 
|-
 
|-
|March 24
+
|Oct. 12
| Spring Break
+
|Marissa Loving
|  
+
|Least dilatation of pure surface braids
|  
+
|(Kent)
 
|-
 
|-
|March 31
+
|Oct. 19
|
+
|Sara Maloni
|  
+
|On type-preserving representations of thrice punctured projective plane group
|  
+
|(Kent)
 
|-
 
|-
|April 7
+
|Oct. 26
|
+
|Dingxin Zhang (Harvard-CMSA)
|  
+
|Relative cohomology and A-hypergeometric equations
|  
+
|(Huang)
 
|-
 
|-
|April 14
+
|Nov. 9
|
+
|Zhongshan An (Stony Brook)
|  
+
|Ellipticity of the Bartnik Boundary Conditions
|  
+
|(Huang)
 
|-
 
|-
|April 21
+
|Nov. 16
+
|Xiangdong Xie
|
+
|Quasi-isometric rigidity of a class of right angled Coxeter groups
|  
+
|(Dymarz)
|-
 
|April 28
 
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)
 
| [[#Bena Tshishiku| "TBA"]]
 
| [http://www.math.wisc.edu/~dymarz Dymarz]
 
 
|-
 
|-
 
|
 
|
 
|}
 
|}
  
== Fall Abstracts ==
 
  
=== Ronan Conlon ===
+
==Spring Abstracts==
''New examples of gradient expanding K\"ahler-Ricci solitons''
+
 
 +
===Mark Pengitore===
 +
 
 +
"Translation-like actions on nilpotent groups"
 +
 
 +
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.
 +
 
 +
===José Ignacio Cogolludo Agustín===
  
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).
+
"Even Artin Groups, cohomological computations and other geometrical
 +
properties."
  
 +
The purpose of this talk is to introduce even Artin groups and consider
 +
their quasi-projectivity properties, as well as study the cohomological
 +
properties of their kernels, that is, the kernels of their characters.
  
=== Jiyuan Han ===
+
===Yan Xu===
''Deformation theory of scalar-flat ALE Kahler surfaces''
+
"Structure of minimal two-spheres of constant curvature in hyperquadrics"
  
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.
+
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.
  
=== Sean Howe ===
+
== Fall Abstracts ==
''Representation stability and hypersurface sections''
 
  
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}!
+
===Teddy Einstein===
=== Nan Li ===
 
''Quantitative estimates on the singular sets of Alexandrov spaces''
 
  
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber.
+
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"
  
=== Yu Li ===
+
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.
  
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature.
+
===Marissa Loving===
  
=== Gaven Marin ===
+
"Least dilatation of pure surface braids"
''TBA''
 
  
=== Peyman Morteza ===
+
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.
''TBA''
 
  
=== Richard Kent ===
+
===Sara Maloni===
''Analytic functions from hyperbolic manifolds''
 
  
Thurston's Geometrization Conjecture, now a celebrated theorem of Perelman, tells us that most 3-manifolds are naturally geometric in nature.  In fact, most 3-manifolds admit hyperbolic metrics.  In the 1970s, Thurston proved the Geometrization conjecture in the case of Haken manifolds, and the proof revolutionized 3-dimensional topology, hyperbolic geometry, Teichm&uuml;ller theory, and dynamics.  Thurston's proof is by induction, constructing a hyperbolic structure from simpler pieces. At the heart of the proof is an analytic function called the ''skinning map'' that one must understand in order to glue hyperbolic structures together.  A better understanding of this map would more brightly illuminate the interaction between topology and geometry in dimension three.  I will discuss what is currently known about this map.
+
"On type-preserving representations of thrice punctured projective plane group"
  
=== Caglar Uyanik ===
+
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.)
''TBA''
 
  
=== Bing Wang ===
+
===Dingxin Zhang===
''The extension problem of the mean curvature flow''
+
"Relative cohomology and A-hypergeometric equations"
  
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.
+
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.
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.
 
This is a joint work with Haozhao Li.
 
  
=== Ben Weinkove ===
 
''Gauduchon metrics with prescribed volume form''
 
  
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric.  I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation.  This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.
+
===Zhongshan An===
 +
"Ellipticity of the Bartnik Boundary Conditions"
  
=== Jonathan Zhu ===
+
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.
''Entropy and self-shrinkers of the mean curvature flow''
 
  
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.
+
===Xiangdong Xie===
 +
"Quasi-isometric rigidity of a class of right angled Coxeter groups"
  
 +
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
 +
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).
 +
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.
  
 
== Spring Abstracts ==
 
== Spring Abstracts ==
 
===Bena Tshishiku===
 
"TBA"
 
  
 
== Archive of past Geometry seminars ==
 
== Archive of past Geometry seminars ==
 +
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]
 +
<br><br>
 +
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
 +
<br><br>
 
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]
 
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]
 
<br><br>
 
<br><br>

Latest revision as of 13:34, 17 April 2019

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Shaosai Huang.

Hawk.jpg


Spring 2019

date speaker title host(s)
April 5 Mark Pengitore (Ohio) Translation-like actions on nilpotent groups (Dymarz)
April 18 José Ignacio Cogolludo Agustín (Universidad de Zaragoza) Even Artin Groups, cohomological computations and other geometrical properties. (Maxim) Unusual date and time: B309 Van Vleck, 2:15-3:15
April 19 Yan Xu (University of Missouri - St. Louis) Structure of minimal two-spheres of constant curvature in hyperquadrics (Huang)

Fall 2018

date speaker title host(s)
Sept. 14 Teddy Einstein (UIC) Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes (Dymarz)
Oct. 12 Marissa Loving Least dilatation of pure surface braids (Kent)
Oct. 19 Sara Maloni On type-preserving representations of thrice punctured projective plane group (Kent)
Oct. 26 Dingxin Zhang (Harvard-CMSA) Relative cohomology and A-hypergeometric equations (Huang)
Nov. 9 Zhongshan An (Stony Brook) Ellipticity of the Bartnik Boundary Conditions (Huang)
Nov. 16 Xiangdong Xie Quasi-isometric rigidity of a class of right angled Coxeter groups (Dymarz)


Spring Abstracts

Mark Pengitore

"Translation-like actions on nilpotent groups"

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.

José Ignacio Cogolludo Agustín

"Even Artin Groups, cohomological computations and other geometrical properties."

The purpose of this talk is to introduce even Artin groups and consider their quasi-projectivity properties, as well as study the cohomological properties of their kernels, that is, the kernels of their characters.

Yan Xu

"Structure of minimal two-spheres of constant curvature in hyperquadrics"

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.

Fall Abstracts

Teddy Einstein

"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"

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.

Marissa Loving

"Least dilatation of pure surface braids"

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.

Sara Maloni

"On type-preserving representations of thrice punctured projective plane group"

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.)

Dingxin Zhang

"Relative cohomology and A-hypergeometric equations"

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.


Zhongshan An

"Ellipticity of the Bartnik Boundary Conditions"

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.

Xiangdong Xie

"Quasi-isometric rigidity of a class of right angled Coxeter groups"

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 as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v). 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.

Spring Abstracts

Archive of past Geometry seminars

2017-2018 Geometry_and_Topology_Seminar_2017-2018

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology