Seminars and Colloquia by Series

Acylindrical hyperbolicity of non-elementary convergence groups

Series
Geometry Topology Seminar
Time
Friday, February 1, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bin Sun – Vanderbilt
The notion of an acylindrically hyperbolic group was introduced by Osin as a generalization of non-elementary hyperbolic and relative hyperbolic groups. Ex- amples of acylindrically hyperbolic groups can be found in mapping class groups, outer automorphism groups of free groups, 3-manifold groups, etc. Interesting properties of acylindrically hyperbolic groups can be proved by applying techniques such as Monod-Shalom rigidity theory, group theoretic Dehn filling, and small cancellation theory. We have recently shown that non-elementary convergence groups are acylindrically hyperbolic. This result opens the door for applications of the theory of acylindrically hyperbolic groups to non-elementary convergence groups. In addition, we recovered a result of Yang which says a finitely generated group whose Floyd boundary has at least 3 points is acylindrically hyperbolic.

Joint GT-UGA Seminar at UGA - Link Floer homology and the stabilization distance

Series
Geometry Topology Seminar
Time
Monday, January 28, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Ian Zemke – Princeton University
In this talk, we describe some applications of link Floer homology to the topology of surfaces in 4-space. If K is a knot in S^3, we will consider the set of surfaces in B^4 which bound K. This space is naturally endowed with a plethora of non-Euclidean metrics and pseudo-metrics. The simplest such metric is the stabilization distance, which is the minimum k such that there is a stabilization sequence connecting two surfaces such that no surface in the sequence has genus greater than k. We will talk about how link Floer homology can be used to give lower bounds, as well as some techniques for computing non-trivial examples. This is joint work with Andras Juhasz.

Joint GT-UGA Seminar at UGA - Knot Concordances in S^1 x S^2 and Constructing Akbulut-Ruberman Type Exotic 4-Manifolds

Series
Geometry Topology Seminar
Time
Monday, January 28, 2019 - 14:30 for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Eylem Yildiz – Michigan State University
I will discuss knot concordances in 3-manifolds. In particular I will talk about knot concordances of knots in the free homotopy class of S^1 x {pt} in S^1 x S^2. It turns out, we can use some of these concordances to construct Akbulut-Ruberman type exotic 4-manifolds. As a consequence, at the end of the talk we will see absolutely exotic Stein pair of 4-manifolds. This is joint work with Selman Akbulut.

Maximal Weinstein domains

Series
Geometry Topology Seminar
Time
Monday, December 3, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Oleg Lazarev – Columbia
Weinstein cobordisms give a natural relationship on the set of Weinstein domains. Flexible Weinstein domains are minimal with respect to this relationship. In this talk, I will use these minimal domains to construct maximal Weinstein domains: any two high-dimensional Weinstein domains with the same topology are Weinstein subdomains of a maximal Weinstein domain also with the same topology. Using this construction, a wide range of new Weinstein domains can be produced, for example exotic cotangent bundles of spheres containing many different closed exact Lagrangians. On the other hand, I will explain how the same line of ideas can be used to prove restrictions on which categories can arise as the Fukaya categories of certain Weinstein domains.

The arithmetic of orientation-reversing mapping classes

Series
Geometry Topology Seminar
Time
Monday, November 19, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Livio Liechti – Paris-Jussieu
Mapping classes are the natural topological symmetries of surfaces. Their study is often restricted to the orientation-preserving ones, which form a normal subgroup of index two in the group of all mapping classes. In this talk, we discuss orientation-reversing mapping classes. In particular, we show that Lehmer's question from 1933 on Mahler measures of integer polynomials can be reformulated purely in terms of a comparison between orientation-preserving and orientation-reversing mapping classes.

Counting incompressible surfaces and the 3D-index

Series
Geometry Topology Seminar
Time
Friday, November 16, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stavros Garoufalidis – Georgia Tech and MPI
I will explain some connections between the counting of incompressible surfaces in hyperbolic 3-manifolds with boundary and the 3Dindex of Dimofte-Gaiotto-Gukov. Joint work with N. Dunfield, C. Hodgson and H. Rubinstein, and, as usual, with lots of examples and patterns.

Affine Grassmannians in motivic homotopy theory

Series
Geometry Topology Seminar
Time
Monday, November 12, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tom Bachmann – MIT
It is a classical theorem in algebraic topology that the loop space of a suitable Lie group can be modeled by an infinite dimensional variety, called the loop Grassmannian. It is also well known that there is an algebraic analog of loop Grassmannians, known as the affine Grassmannian of an algebraic groop (this is an ind-variety). I will explain how in motivic homotopy theory, the topological result has the "expected" analog: the Gm-loop space of a suitable algebraic group is A^1-equivalent to the affine Grassmannian.

A family of freely slice good boundary links

Series
Geometry Topology Seminar
Time
Monday, November 5, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Min Hoon Kim – Korea Institute for Advanced Study
The still open topological 4-dimensional surgery conjecture is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.

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