Seminars and Colloquia by Series

Uniform perfection: a DIFF-icult situation

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).

The Braid Group and the Burau Representation

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

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.

Everything Alexander in the context of mapping class group

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.

The cohomological dimension of the terms of the Johnson filtration

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 –

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.

3-Manifolds up to 1957

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 –

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.

Morphisms of Curve Graphs and Surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, April 20, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Katherine Booth – Georgia Tech

Ivanov’s metaconjecture says that every object naturally associated to a surface S with a sufficiently rich structure has the mapping class group as its group of automorphisms. In this talk, I will present several cases of curve graphs that satisfy this metaconjecture and some extensions to even richer structures.

An exotic contractible 4 manifold

Series
Geometry Topology Student Seminar
Time
Wednesday, February 23, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sierra Knavel – Georgia Tech

We will discuss Akbulut's construction of two smooth, contractible four-manifolds whose boundaries are diffeomorphic and extend to a homeomorphism but not to a diffeomorphism of the manifolds. 

Topological Methods in Convexity

Series
Geometry Topology Student Seminar
Time
Wednesday, February 16, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin Shu – Georgia Tech

Topological methods have had a rich history of use in convex optimization, including for instance the famous Pataki-Barvinok bound on the ranks of solutions to semidefinite programs, which involves the Borsuk-Ulam theorem. We will give two proofs of a similar sort involving the use of some basic homotopy theory. One is a new proof of Brickman's theorem, stating that the image of a sphere into R^2 under a quadratic map is convex, and the other is an original theorem stating that the image of certain matrix groups under linear maps into R^2 is convex. We will also conjecture some higher dimensional analogues.

The slice-ribbon conjecture and 3-stranded pretzel knots

Series
Geometry Topology Student Seminar
Time
Wednesday, February 9, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hugo Zhou – Georgia Tech

This is an expository talk about the slice-ribbon conjecture. A knot is slice if it bounds a disk in the four ball. We call a slice knot ribbon if it bounds a slice disk with no local maxima. The slice-ribbon conjecture asserts all slice knots arise in this way. We also give a very brief introduction to Greene, Jabuka and Lecuona's works on the slice-ribbon conjecture for 3-stranded pretzel knots.

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