Geometry and Topology Seminar 2019-2020
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Richard Kent.
Fall 2012
| date | speaker | title | host(s) |
|---|---|---|---|
| September 21 | Owen Sizemore (Wisconsin) | local | |
| September 28 | Mireille Boutin (Purdue) | Mari Beffa | |
| October 5 | Ben Schmidt (Michigan State) | Dymarz | |
| October 12 | Ian Biringer (Boston College) |
Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence |
Dymarz |
| October 19 | Peng Gao (Simons Center for Geometry and Physics) | Wang | |
| October 26 | Jo Nelson (Wisconsin) |
Cylindrical contact homology as a well-defined homology theory? Part I |
local |
| November 2 | Jennifer Taback (Bowdoin) |
The geometry of twisted conjugacy classes in Diestel-Leader groups |
Dymarz |
| November 9 | Jenny Wilson (Chicago) | Ellenberg | |
| November 16 | Jonah Gaster (UIC) | Kent | |
| Thanksgiving Recess | |||
| November 30 | Shinpei Baba (Caltech) | Kent | |
| December 7 | Kathryn Mann (Chicago) | Kent | |
| December 14 |
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)
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- 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.
Ben Schmidt (Michigan State)
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.
Ian Biringer (Boston College)
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)
TBA
Shinpei Baba (Caltech)
TBA
Kathryn Mann (Chicago)
TBA
Spring 2013
| date | speaker | title | host(s) |
|---|---|---|---|
| January 25 | |||
| February 1 | |||
| February 8 | |||
| February 15 | |||
| February 22 | |||
| March 1 | |||
| March 8 | |||
| March 15 | |||
| March 22 | Michelle Lee (Michigan) | Kent | |
| Spring Break | |||
| April 5 | |||
| April 12 | |||
| April 19 | |||
| April 26 | |||
| May 3 | |||
| May 10 |
Spring Abstracts
Michelle Lee (Michigan)
TBA
Archive of past Geometry seminars
2011-2012: Geometry_and_Topology_Seminar_2011-2012
2010: Fall-2010-Geometry-Topology