Seminars and Colloquia by Series

An Alexander method for infinite-type surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, April 21, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Roberta Shapiro

Given a surface S, the Alexander method is a combinatorial tool used to determine whether two homeomorphisms are isotopic. This statement was formalized in A Primer on Mapping Class Groups in the case that S is of finite type. We extend the Alexander method to include infinite-type surfaces, which are surfaces with infinitely generated fundamental groups.

In this talk, we will introduce a technique useful in proofs dealing with infinite-type surfaces. Then, we provide a "proof by example" of an infinite-type analogue of the Alexander method.

Exotic smooth structures and H-slice knots

Series
Geometry Topology Student Seminar
Time
Wednesday, April 7, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Hyunki MinGeorgia Tech

One of interesting topic in low-dimensional topology is to study exotic smooth structures on closed 4-manifolds. In this talk, we will see an example to distinguish exotic smooth structure using H-slice knots.

Symplectic rigidity, flexibility, and embedding problems

Series
Geometry Topology Student Seminar
Time
Wednesday, March 31, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Agniva RoyGeorgia Tech

Embedding problems, of an n-manifold into an m-manifold, can be heuristically thought to belong to a spectrum, from rigid, to flexible. Euclidean embeddings define the rigid end of the spectrum, meaning you can only translate or rotate an object into the target. Symplectic embeddings, depending on the object, and target, can show up anywhere on the spectrum, and it is this flexible vs rigid philosophy, and techniques developed to study them, that has lead to a lot of interesting mathematics. In this talk I will make this heuristic clearer, and show some examples and applications of these embedding problems.

Introduction to Knot Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, March 17, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Weizhe Shen

Knot Floer homology is an invariant for knots introduced by Ozsváth-Szabó and, independently, Rasmussen.  We will give a general introduction to the theory, sketching the definition and highlight its major properties and applications.

Snowflake Conjectures for Mapping Class Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, March 3, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Santana Afton

The algebraic structure of mapping class groups is deep and beautiful; in this talk, we'll explore some curious conjectures and definite theorems about the structure and quality of different subgroups of the mapping class group.

Quantum Teichmüller space in shear coordinates

Series
Geometry Topology Student Seminar
Time
Wednesday, February 3, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Tao YuGatech

The Teichmüller space is the space of hyperbolic structures on surfaces, and there are different flavors depending on the class of surfaces. In this talk we consider the enhanced Teichmüller space which includes additional data at boundary components. The enhanced version can be parametrized by shear coordinates, and in these coordinates, the Weil-Peterson Poisson structure has a simple form. We will discuss a construction of the quantum Teichmüller space corresponding to this Poisson structure.

 

Bluejeans: https://bluejeans.com/872588027

Serre Spectral Sequence

Series
Geometry Topology Student Seminar
Time
Wednesday, January 27, 2021 - 14:00 for
Location
ONLINE
Speaker
Hugo Zhou

I will introduce Serre spectral sequences, then compute some examples. The talk will be in most part following Allen Hatcher's notes on spectral sequences.

The Akbulut-Kirby conjecture and the slice-ribbon conjecture

Series
Geometry Topology Student Seminar
Time
Wednesday, December 2, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Weizhe Shen

A knot in the 3-sphere is slice if it bounds a smooth disc in the 4-ball. A knot is ribbon if it bounds a self-intersecting disc with only singularities that are closed arcs consisting of intersection points of the disc with itself. Every ribbon knot is a slice knot; the converse is a famous unsolved conjecture of Fox. This talk will show some recent interesting progress around the slice-ribbon conjecture.

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