Seminars and Colloquia by Series

Generalized Schönflies theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, January 31, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – GaTech
The Jordan curve theorem states that any simple closed curve decomposes the 2-sphere into two connected components and is their common boundary. Schönflies strengthened this result by showing that the closure of either connected component in the 2-sphere is a 2-cell. While the first statement is true in higher dimensions, the latter is not. However under the additional hypothesis of locally flatness, the closure of either connected component is an n-cell. This result is called the Generalized Schönflies theorem, and was proved independently by Morton Brown and Barry Mazur. In this talk, I will describe the proof of due to Morton Brown.

Interval self-maps: what you knead to know

Series
Geometry Topology Student Seminar
Time
Wednesday, January 24, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Lanier – GaTech
Take a map from the interval [0,1] to itself. Such a map can be iterated, and many phenomena (such as periodic points) arise. An interval self-map is an example of a topological dynamical system that is simple enough to set up, but wildly complex to analyze. In the late 1970s, Milnor and Thurston developed a combinatorial framework for studying interval self-maps in their paper "Iterated maps of the interval". In this talk, we will give an introduction to the central questions in the study of iterated interval maps, share some illustrative examples, and lay out some of the techniques and results of Milnor and Thurston.

Survey on 3-manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, November 29, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee – Georgia Tech
I'll try to describe some known facts about 3 manifolds. And in the end I want to give some idea about Geometrization Conjecture/theorem.

Taut foliations and Sutured Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 15, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Tech
It is known that a class of codimension one foliations, namely "taut foliations", have subtle relation with the topology of a 3-manifold. In early 80s, David Gabai introduced the theory of "sutured manifolds" to study these objects and more than 20 years later, Andres Juhasz developed a Floer type theory, namely "Sutured Floer Homology", that turned out to be very useful in answering the question of when a 3-manifold with boundary supports a taut foliation.

A discussion of the the Lickorish Wallace Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 8, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva Roy – Georgia Tech
The Lickorish Wallace Theorem states that any closed 3-manifold is the result of a +/- 1-surgery on a link in S^3. I shall discuss the relevant definitions, and present the proof as outlined in Rolfsen's text 'Knots and Links' and Lickorish's 'Introduction to Knot Theory'.

Lens space realization problem

Series
Geometry Topology Student Seminar
Time
Wednesday, October 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech
I will talk about the Berge conjecture, and Josh Greene's resolution of a related problem, about which lens spaces can be obtained by integer surgery on a knot in S^3.

Computing Heegaard Floer homology by factoring mapping classes

Series
Geometry Topology Student Seminar
Time
Wednesday, October 11, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Lanier – Georgia Tech
We will discuss the mapping class groupoid, how it is generated by handle slides, and how factoring in the mapping class groupoid can be used to compute Heegaard Floer homology. This talk is based on work by Lipshitz, Ozsvath, and Thurston.

The Alexander polynomial

Series
Geometry Topology Student Seminar
Time
Wednesday, October 4, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Libby Taylor – Georgia Tech
Let K be a tame knot in S^3. Then the Alexander polynomial is knot invariant, which consists of a Laurent polynomial arising from the infinite cyclic cover of the knot complement. We will discuss the construction of the Alexander polynomial and, more generally, the Alexander invariant from a Seifert form on the knot. In addition, we will see some connections between the Alexander polynomial and other knot invariants, such as the genus and crossing number.

Null-Homotopic Embedded Spheres of Codimenion One

Series
Geometry Topology Student Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee – Georgia Tech
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.

Braided embeddings of manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, September 20, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech
The theory of braids has been very useful in the study of (classical) knot theory. One can hope that higher dimensional braids will play a similar role in higher dimensional knot theory. In this talk we will introduce the concept of braided embeddings of manifolds, and discuss some natural questions about them.

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