### TBA

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, April 5, 2023 - 14:00 for
- Location
- Skiles 006
- Speaker
- Alex Nolte – Rice

TBD

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- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, April 5, 2023 - 14:00 for
- Location
- Skiles 006
- Speaker
- Alex Nolte – Rice

TBD

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, March 15, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Speaker

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, March 8, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Roberta Shapiro – Georgia Tech – rshapiro32@gatech.edu

The pants complex of a surface has as its 0-cells the pants decompositions of a surface and as its 1-cells some elementary moves relating two pants decompositions; the 2-cells are disks glued along certain cycles in the 1-skeleton of the complex. In "Pants Decompositions of Surfaces," Hatcher proves that this complex is contractible.

During this interactive talk, we will aim to understand the structure of the pants complex and some of the important tools that Hatcher uses in his proof of contractibility.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, March 1, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Cindy Tan – University of Chicago – cindy@math.uchicago.edu

When do commuting homeomorphisms of S^2 have a common fixed point? Christian Bonatti gave the first sufficient condition: Commuting diffeomorphisms sufficiently close to the identity in Diff^+(S^2) always admit a common fixed point. In this talk we present a result of Michael Handel that extends Bonatti's condition to a much larger class of commuting homeomorphisms. If time permits, we survey results for higher genus surfaces due to Michael Handel and Morris Hirsch, and connections to certain compact foliated 4-manifolds.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, February 15, 2023 - 14:00 for
- Location
- Skiles 006
- Speaker
- Roberta Shapiro – Georgia Tech

Have you ever wanted to marry topology, hyperbolic geometry, and geometric group theory, all at once?* Bowden-Hensel-Webb do this and more when they embark on their study of Diff0(S). In this talk, we will discuss the main theorems of Bowden-Hensel-Webb's paper, the most notable of which is (arguably) the lack of uniform perfection of Diff0(S). We will then summarize the main tools they use to prove these results. (Note: the perspectives on Diff0(S) in this talk will DIFFer greatly from those used in the diffeomorphism groups class.)

*If you answered "yes" for your personal life as opposed to your academic life: that's ok, I won't judge (if you don't tell me).

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, February 8, 2023 - 14:00 for
- Location
- Speaker
- Jacob Guynee – Georgia Tech – dsminahan@gmail.com

The braid group has many applications throughout the world of math due to its simple yet rich structure. In this talk we will focus on the Burau representation of the braid group, which has important implications in knot theory. Most notably, the open problem of faithfulness of the Burau representation of the braid group on 4 strands is equivalent to whether or not the Jones polynomial can detect the unknot. The Burau representation has a topological interpretation that uses the mapping class definition of the braid group. We'll introduce the braid group first and then discuss the Burau representation. We will go through examples for small n and discuss the proof of nonfaithfulness for n > 4. Time permitting, we may introduce the Gassner representation.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, November 30, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jaden Wang – Georgia Tech

Disks are nice for many reasons. In this casual talk, I will try to convince you that it's even nicer than you think by presenting the Alexander's lemma. Just like in algebraic topology, we are going to rely on disks heavily to understand mapping class groups of surfaces. The particular method is called the Alexander's method. Twice the Alexander, twice the fun! No background in mapping class group is required.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, October 26, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Dan Minahan – Georgia Tech – dminahan6@gatech.edu

Abstract: How big is a group? One possible notion of the size of the group is the cohomological dimension, which is the largest n for which a group G can have non—trivial cohomology in degree n, possibly with twisted coefficients. Following the work of Bestvina, Bux and Margalit, we compute the cohomological dimension of the terms Johnson filtration of a closed surface. No background is required for this talk.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, October 12, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- TBA

TBA

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, October 5, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Weizhe Shen – Georgia Institute of Technology – wshen41@gatech.edu

**Please Note:** A three-manifold is a space that locally looks like the Euclidean three-dimensional space. The study of three-manifolds has been at the heart of many beautiful constructions in low dimensional topology. This talk will provide a quick tour through some fundamental results about three-manifolds that were discovered between the late nineteenth century and the Fifties.