Seminars and Colloquia by Series

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.

Teichmüller space via skein algebras

Series
Geometry Topology Student Seminar
Time
Wednesday, February 2, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Tao Yu – Georgia Tech

Quantum Teichmüller space was first introduced by Chekhov and Fock as a version of 2+1d quantum gravity. The definition was translated over time into an algebra of curves on surfaces, which coincides with an extension of the Kauffman bracket skein algebra. In this talk, we will discuss the relation between the Teichmüller space and the Kauffman bracket, and time permitting, the quantized version of this correspondence.

Meeting URL: https://bluejeans.com/106460449/5822

 

An introduction to Cork twists, Gluck twists, and Logarithmic transformations of 4-manifolds.

Series
Geometry Topology Student Seminar
Time
Wednesday, December 1, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Sierra Knavel – Georgia Tech

Please Note: BlueJeans link: https://bluejeans.com/609527728/0740

The main goal of manifold theory is to classify all n-dimensional topological manifolds. For a smooth 4-manifold X, we aim to understand all of the exotic smooth structures there are to the smooth structure on X. Exotic smooth structures are homeomorphic but not diffeomorphic. Cork twists, Gluck twists, and Log transforms are all ways to construct possible exotic pairs by re-gluing embedded surfaces in the 4-manifold. In this talk, we define these three constructions.  

Pages