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.
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The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
<br>
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<br>  
For more information, contact [http://www.math.wisc.edu/~rkent Richard Kent].
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For more information, contact Shaosai Huang.
  
 
[[Image:Hawk.jpg|thumb|300px]]
 
[[Image:Hawk.jpg|thumb|300px]]
  
== Spring 2013 ==
 
  
 
{| cellpadding="8"
 
!align="left" | date
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
|-
 
|January 25
 
| [http://www.maths.usyd.edu.au/u/athomas/ Anne Thomas] (Sydney)
 
| [[#Anne Thomas (Sydney)| ''Divergence in right-angled Coxeter groups'']]
 
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
|-
 
|February 1
 
|
 
|
 
|
 
|-
 
|February 8
 
|
 
|
 
|
 
|-
 
|February 15
 
| [http://www3.nd.edu/~lnicolae/ Liviu Nicolaescu] (Notre Dame)
 
| [[#Liviu Nicolaescu (Notre Dame)| ''Random Morse functions and spectral geometry'']]
 
|[http://www.math.wisc.edu/~oh/ Oh]
 
|-
 
|February 22
 
|
 
|
 
|
 
|-
 
|March 1
 
| [https://pantherfile.uwm.edu/chruska/www/ Chris Hruska] (UW Milwaukee)
 
| [[#Chris Hruska (UW Milwaukee)| ''Local topology of boundaries and isolated flats'']]
 
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
|-
 
|March 8
 
|
 
|
 
|
 
|-
 
|March 11, <b>MONDAY in B113!</b>
 
| [http://www.math.fsu.edu/~hironaka/ Eriko Hironaka] (FSU)
 
| [[#Eriko Hironaka (FSU)| ''Small dilatation pseudo-Anosov mapping classes'']]
 
|[http://www.math.wisc.edu/~rkent/ Kent]
 
|-
 
|March 15
 
| Yu-Shen Lin (Harvard)
 
| [[#Yu-Shen Lin (Harvard)| ''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing'']]
 
| [http://www.math.wisc.edu/~oh/ Oh]
 
|-
 
|March 20 <b>WEDNESDAY in 901!</b>
 
|[http://www.math.nyu.edu/faculty/cappell/index.html Sylvain Cappell] (NYU)
 
|[[#Sylvain Cappell (NYU)| ''Topological actions of compact, connected Lie Groups on Manifolds'']]
 
| [http://www.math.wisc.edu/~maxim/ Maxim]
 
|-
 
|Spring Break
 
|
 
|
 
|
 
|-
 
|April 5
 
|
 
|
 
|
 
|-
 
|April 12
 
|Manuel Gonzalez Villa (Heidelberg)
 
|''The monodromy conjecture for plane meromorphic germs''
 
|Laurentiu
 
|-
 
|April 19
 
|
 
|
 
|
 
|-
 
|April 26
 
| Emmy Murphy (MIT)
 
| [[#Emmy Murphy| ''Exact Lagrangian immersions with few transverse self intersections'']]
 
| [http://www.math.wisc.edu/~oh/ Oh]
 
|-
 
|May 3
 
| Yuan-qi Wang (UCSB)
 
| [[#Yuan-qi Wang (UCSB)| ''TBA'']]
 
| [http://www.math.wisc.edu/~bwang/ Wang]
 
|-
 
|
 
|
 
|-
 
|May 10
 
| [http://www.math.wisc.edu/~oh/ Yong-Geun Oh] (Wisconsin)
 
| [[#Yong-Geun Oh| ''TBA'']]
 
| Local
 
|-
 
|}
 
 
== Spring Abstracts ==
 
 
===Anne Thomas (Sydney)===
 
''Divergence in right-angled Coxeter groups''
 
 
Abstract:
 
The divergence of a pair of geodesic rays emanating from a point is a
 
measure of how quickly they are moving away from each other. In
 
Euclidean space divergence is linear, while in hyperbolic space
 
divergence is exponential. Gersten used this idea to define a
 
quasi-isometry invariant for groups, also called divergence, which has
 
been investigated for classes of groups including fundamental groups
 
of 3-manifolds, mapping class groups and right-angled Artin groups. I
 
will discuss joint work with Pallavi Dani on divergence in
 
right-angled Coxeter groups (RACGs).  We characterise 2-dimensional
 
RACGs with quadratic divergence, and prove that for every positive
 
integer d, there is a RACG with divergence polynomial of degree d.
 
 
===Liviu Nicolaescu (Notre Dame)===
 
''Random Morse functions and spectral geometry''
 
 
Abstract:
 
I will discuss the distribution of critical values of a  smooth random function on a compact m-dimensional Riemann manifold (M,g)  described as a random  superposition  of eigenfunctions of the Laplacian.  The  notion of randomness that we use    has a naturally  built in  small parameter $\varepsilon$, and we show that    as $\varepsilon\to 0$ the distribution of critical  values closely resemble the distribution  of eigenvalues  of  certain  random symmetric  $(m+1)\times (m+1)$-matrices  of the type introduced by E. Wigner  in quantum mechanics. Additionally, I will  explain how to recover the metric  $g$ from  statistical  properties of the Hessians of the above random function.
 
 
===Chris Hruska (UW Milwaukee)===
 
''Local topology of boundaries and isolated flats''
 
 
Abstract:  Swarup proved that every one-ended word hyperbolic group has a
 
locally connected Gromov boundary.  However for CAT(0) groups,
 
non-locally connected boundaries are easy to construct.  For instance
 
the boundary of F_2 x Z is the suspension of a Cantor set.
 
 
In joint work with Kim Ruane, we have studied boundaries of CAT(0)
 
spaces with isolated flats.  If G acts properly, cocompactly on such a
 
space X, we give a necessary and sufficient condition on G such that
 
the boundary of X is locally connected.  As a corollary, we deduce
 
that such a group G is semistable at infinity.
 
 
===Eriko Hironaka (FSU)===
 
''Small dilatation pseudo-Anosov mapping classes''
 
 
The theory of fibered faces implies that  pseudo-Anosov
 
mapping classes with bounded normalized dilatation can be partitioned
 
into a finite number of families with related dynamics.  In this talk we
 
discuss the problem of finding concrete description
 
of the members of these families.  One conjectural way generalizes a
 
well-known sequence
 
defined by Penner in '91.  However, so far no known examples  of
 
this type come close to
 
the smallest known accumulation point of normalized dilatations.
 
In this talk we describe a different construction that uses mixed-sign
 
Coxeter systems.  A deformation of the simplest pseudo-Anosov braid monodromy
 
can be obtained in this way, and hence this model does realize the
 
smallest known accumulation point.
 
 
===Yu-Shen Lin (Harvard)===
 
''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing''
 
 
Strominger-Yau-Zaslow conjecture suggests that the Ricci-flat metric on Calabi-Yau manifolds might be related to holomorphic discs. In this talk, I will define a new open Gromov-Witten invariants on elliptic K3 surfaces trying to explain this conjecture. The new invariant satisfies certain wall-crossing formula and multiple cover formula. I will also establish a tropical-holomorphic correspondence. Moreover, this invariant is expected to be equivalent to the generalized Donaldson-Thomas invariants in the hyperK\"ahler metric constructed by Gaiotto-Moore-Neitzke. If time allowed, I will talk about the connection with disks counting on Calabi-Yau 3-folds.
 
 
===Sylvain Cappell (NYU)===
 
''TBA''
 
 
===Yong-Geun Oh (Wisconsin)===
 
''TBA''
 
 
===Emmy Murphy (MIT)===
 
''Exact Lagrangian immersions with few transverse self intersections''
 
 
This talk will focus on the following question: supposing a
 
smooth manifold immerses into C^n as an exact Lagrangian, what is the
 
minimal number of transverse self-intersections necessary? Finding lower
 
bounds on the number of intersections of two embedded Lagrangians is a
 
central problem in symplectic topology which has seen much success; in
 
contrast bounding the number of self-intersections of an exact Lagrangian
 
immersion requires more advanced tools and the known results are far less
 
general. We show that no Arnold-type lower bound exists for exact
 
Lagrangian immersions by constructing examples with surprisingly few
 
self-intersections. For example, we show that any three-manifold immerses
 
as an exact Lagrangian in C^3 with a single transverse self-intersection.
 
We also apply Lagrangian surgery to these immersions to give some
 
interesting new examples of Lagrangian embeddings. (This is joint work of
 
the speaker with T. Ekholm, Y. Eliashberg, and I. Smith.)
 
 
===Yuan-qi Wang (UCSB)===
 
''TBA''
 
 
== Fall 2012==
 
  
  
 +
== Fall 2019 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 201: Line 16:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 21
+
|Oct. 4
| [http://www.math.wisc.edu/~josizemore/ Owen Sizemore] (Wisconsin)
+
|Ruobing Zhang (Stony Brook University)
| [[#Owen Sizemore (Wisconsin) |
+
| Geometric analysis of collapsing Calabi-Yau spaces
''Operator Algebra Techniques in Measureable Group Theory'']]
+
|(Chen)
| local
 
 
|-
 
|-
|September 28
 
|[https://engineering.purdue.edu/~mboutin/ Mireille Boutin] (Purdue)
 
|[[#Mireille Boutin (Purdue) |
 
''The Pascal Triangle of a discrete Image: <br>
 
definition, properties, and application to object segmentation'']]
 
|[http://www.math.wisc.edu/~maribeff/ Mari Beffa]
 
 
|-
 
|-
|October 5
+
|Oct. 25
| [http://www.math.msu.edu/~schmidt/ Ben Schmidt] (Michigan State)
+
|Emily Stark (Utah)
| [[#Ben Schmidt (Michigan State)|
+
| TBA
''Three manifolds of constant vector curvature'']]
+
|(Dymarz)
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
 
|-
 
|-
|October 12
+
|Nov. 8
| [https://www2.bc.edu/ian-p-biringer/ Ian Biringer] (Boston College)
+
|Max Forester (University of Oklahoma)
| [[#Ian Biringer (Boston College)|
+
| TBA
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence'']]
+
|(Dymarz)
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
 
|-
 
|-
|October 19
+
|Nov. 22
| Peng Gao (Simons Center for Geometry and Physics)
+
|Yu Li (Stony Brook University)
| [[#Peng Gao (Simons Center for Geometry and Physics)|
+
|On the structure of Ricci shrinkers
''string theory partition functions and geodesic spectrum'']]
+
|(Huang)
|[http://www.math.wisc.edu/~bwang/ Wang]
 
 
|-
 
|-
|October 26
 
| [http://www.math.wisc.edu/~nelson/ Jo Nelson] (Wisconsin)
 
| [[#Jo Nelson (Wisconsin) |
 
''Cylindrical contact homology as a well-defined homology theory? Part I'']]
 
| local
 
|-
 
|November 2
 
| [http://www.bowdoin.edu/~jtaback/ Jennifer Taback] (Bowdoin)
 
| [[#Jennifer Taback (Bowdoin)|
 
''The geometry of twisted conjugacy classes in Diestel-Leader groups'']]
 
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
 
|-
 
|November 9
 
| [http://math.uchicago.edu/~wilsonj/ Jenny Wilson] (Chicago)
 
| [[#Jenny Wilson (Chicago)|
 
''FI-modules for Weyl groups'']]
 
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]
 
|-
 
|November 16
 
|[http://www.math.uic.edu/people/profile?id=GasJ574 Jonah Gaster] (UIC)
 
|[[#Jonah Gaster (UIC)|
 
''A Non-Injective Skinning Map with a Critical Point'']]
 
|[http://www.math.wisc.edu/~rkent/ Kent]
 
|-
 
| Thanksgiving Recess
 
|
 
|
 
|
 
|-
 
|November 30
 
| [http://www.its.caltech.edu/~shinpei/ Shinpei Baba] (Caltech)
 
|[[#Shinpei Baba (Caltech)|
 
''Grafting and complex projective structures'']]
 
|[http://www.math.wisc.edu/~rkent/ Kent]
 
|-
 
|December 7
 
| [http://math.uchicago.edu/~mann/ Kathryn Mann] (Chicago)
 
|[[#Kathryn Mann (Chicago)|
 
''The group structure of diffeomorphism groups'']]
 
|[http://www.math.wisc.edu/~rkent/ Kent]
 
|-
 
|
 
 
|}
 
|}
  
== Fall Abstracts ==
+
==Fall Abstracts==
 
 
===Owen Sizemore (Wisconsin)===
 
''Operator Algebra Techniques in Measureable Group Theory''
 
 
 
Measurable group theory is the study of groups via their actions on measure spaces. While the classification for amenable groups was essentially complete by the early 1980's,  progress for nonamenable groups has been slow to emerge. The last 15 years has seen a surge in the classification of ergodic actions of nonamenable groups, with methods coming from diverse areas. We will survey these new results, as well as, give an introduction to the operator algebra techniques that have been used.
 
  
===Mireille Boutin (Purdue)===
+
===Ruobing Zhang===
''The Pascal Triangle of a discrete Image: definition, properties, and application to object segmentation''
 
  
We define the Pascal Triangle of a discrete (gray scale) image as a pyramidal ar-
+
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.
rangement of complex-valued moments and we explore its geometric significance. In
 
particular, we show that the entries of row k of this triangle correspond to the Fourier
 
series coefficients of the moment of order k of the Radon transform of the image. Group
 
actions on the plane can be naturally prolonged onto the entries of the Pascal Triangle. We study the induced action of some common group actions, such as translation,
 
rotations, and reflections, and we propose simple tests for equivalence and self-
 
equivalence for these group actions. The motivating application of this work is the
 
problem of recognizing ”shapes” on images, for example characters, digits or simple
 
graphics. Application to the MERGE project, in which we developed a fast method for segmenting hazardous material signs on a cellular phone, will be also discussed.  
 
  
This is joint work with my graduate students Shanshan Huang and Andrew Haddad.
+
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.
  
===Ben Schmidt (Michigan State)===
+
===Emily Stark===
''Three manifolds of constant vector curvature.''
 
  
A Riemannian manifold M is said to have extremal curvature K if all sectional curvatures are bounded above by K or if all sectional curvatures are bounded below by K.  A manifold with extremal curvature K has constant vector curvature K if every tangent vector to M belongs to a tangent plane of curvature K.  For surfaces, having constant vector curvature is equivalent to having constant curvature.  In dimension three, the eight Thurston geometries all have constant vector curvature.  In this talk, I will discuss the classification of closed three manifolds with constant vector curvature.  Based on joint work with Jon Wolfson.
+
"TBA"
  
===Ian Biringer (Boston College)===
+
===Max Forester===
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence''
 
 
 
We will describe an asymptotic relationship between the volume and the Betti numbers of certain locally symmetric spaces. The proof uses an exciting new tool: a synthesis of Gromov-Hausdorff convergence of Riemannian manifolds and Benjamini-Schramm convergence from graph theory.
 
 
 
===Peng Gao (Simons Center for Geometry and Physics)===
 
''string theory partition functions and geodesic spectrum''
 
 
 
String theory partition functions often have nice modular properties, which is well understood within the context of representation theory of (supersymmetric extensions) of Virasoro algebra.
 
However, many questions of physical importance are preferrably addressed when string theory is formulated in terms of non-linear sigma model on a Riemann surface with a Riemannian manifold as target space. Traditionally, physicists have studied such sigma models within the realm of perturbation theory, overlooking a large class of very natural critical points of the path integral, namely, closed geodesics on the target space Riemannian manifold. We propose how to take into account the effect of these critical points on the path integral, and initiate its study on Ricci flat targe spaces, such as the K3 surface.
 
 
 
===Jo Nelson (Wisconsin)===
 
''Cylindrical contact homology as a well-defined homology theory? Part I''
 
 
 
In this talk I will define all the concepts in the title, starting with what a contact manifold is.  I will also  explain how the heuristic arguments sketched in the literature since 1999 fail to define a homology theory and provide a foundation for a well-defined cylindrical contact homology, while still providing an invariant of the contact structure.  A later talk will provide us with a large class of examples under which one can compute a well-defined version of cylindrical contact homology via a new approach the speaker developed for her thesis that is distinct and completely independent of previous specialized attempts.
 
 
 
===Jennifer Taback (Bowdoin)===
 
''The geometry of twisted conjugacy classes in Diestel-Leader groups''
 
 
 
The problem of computing the Reidemsieter number R(f)  of a group automorphism f, that is, the number of f-twisted conjugacy classes, is related to questions in Lefschetz-Nielsen fixed point theory.  We say a group has property R-infinity if every group automorphism has infinitely many twisted conjugacy classes.  This property has been studied by Fel’shtyn, Gonzalves, Wong, Lustig, Levitt and others, and has applications outside of topology.
 
 
Twisted conjugacy classes in lamplighter groups are well understood both geometrically and algebraically.  In particular the lamplighter group L_n does not have property R-infinity iff (n,6)=1. In this talk I will extend these results to Diestel-Leader groups with a surprisingly different conclusion.  The family of Diestel-Leader groups provides a natural geometric generalization of the lamplighter groups.  I will define these groups, as well as Diestel-Leader graphs and describe how these results include a computation of the automorphism group of this family.
 
This is joint work with Melanie Stein and Peter Wong.
 
 
 
===Jenny Wilson (Chicago)===
 
''FI-modules for Weyl groups''
 
 
 
Earlier this year, Church, Ellenberg, and Farb developed a new framework for studying sequences of representations of the symmetric groups, using a concept they call an FI--module. I will give an overview of this theory, and describe how it generalizes to sequences of representations of the classical Weyl groups in Type B/C and D. The theory of FI--modules has provided a wealth of new results by numerous authors working in algebra, geometry, and topology. I will outline some of these results, including applications to configurations spaces and groups related to the braid group.
 
 
 
===Jonah Gaster (UIC)===
 
''A Non-Injective Skinning Map with a Critical Point''
 
 
 
Following Thurston, certain classes of 3-manifolds yield holomorphic maps on the Teichmuller spaces of their boundary components. Inspired by numerical evidence of Kent and Dumas, we present a negative result about the regularity of such maps. Namely, we construct a path of deformations of the hyperbolic structure on a genus-2 handlebody, with two rank-1 cusps. The presence of some extra symmetry yields information about the convex core, which is used to conclude some inequalities involving the extremal length of a certain symmetric curve family. The existence of a critical point for the associated skinning map follows.
 
 
 
===Shinpei Baba (Caltech)===
 
''Grafting and complex projective structures''
 
 
 
A complex projective structure is a certain geometric structure on a (real) surface, and it corresponds a representation from the fundamental group of the base surface into PSL(2,C).  We discuss about a certain surgery operation, called a 2&pi;&ndash;grafting, which produces a different projective structure, preserving its holonomy representation.
 
This surgery is closely related to three-dimensional hyperbolic geometry.
 
 
 
===Kathryn Mann (Chicago)===
 
''The group structure of diffeomorphism groups''
 
 
 
Abstract:
 
What is the relationship between manifolds and the structure of their
 
diffeomorphism groups?
 
On the positive side, a remarkable theorem of Filipkiewicz says that the
 
group structure determines the manifold: if Diff(M) and Diff(N) are
 
isomorphic, then M and N are diffeomorphic.
 
On the negative side, we know little else.  Could the group Diff(M) act by
 
diffeomorphisms on M in nonstandard ways?  Does the "size" of Diff(M) say
 
anything about the complexity of M?  Ghys asked if M and N are manifolds,
 
and the group of compactly supported diffeomorphisms of N injects into the
 
group of compactly supported diffeomorphisms of M, can the dimension of M
 
be less than dim(N)?  We'll discuss these and other questions, and answer
 
these in the (already quite rich) case of dim(M)=1.
 
  
 +
“TBA”
  
 +
===Yu Li===
 +
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.
  
 
== Archive of past Geometry seminars ==
 
== Archive of past Geometry seminars ==
 
+
2018-2019  [[Geometry_and_Topology_Seminar_2018-2019]]
 +
<br><br>
 +
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]]
 +
<br><br>
 +
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]
 +
<br><br>
 +
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]
 +
<br><br>
 +
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]
 +
<br><br>
 
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]
 
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]
 
<br><br>
 
<br><br>
 
2010: [[Fall-2010-Geometry-Topology]]
 
2010: [[Fall-2010-Geometry-Topology]]

Latest revision as of 22:01, 24 September 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



Fall 2019

date speaker title host(s)
Oct. 4 Ruobing Zhang (Stony Brook University) Geometric analysis of collapsing Calabi-Yau spaces (Chen)
Oct. 25 Emily Stark (Utah) TBA (Dymarz)
Nov. 8 Max Forester (University of Oklahoma) TBA (Dymarz)
Nov. 22 Yu Li (Stony Brook University) On the structure of Ricci shrinkers (Huang)

Fall Abstracts

Ruobing Zhang

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.

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.

Emily Stark

"TBA"

Max Forester

“TBA”

Yu Li

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.

Archive of past Geometry seminars

2018-2019 Geometry_and_Topology_Seminar_2018-2019

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