Seminars and Colloquia by Series

Convexity and Contact Sphere Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, March 14, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena HozooriGaTech
Assuming some "compatibility" conditions between a Riemannian metric and a contact structure on a 3-manifold, it is natural to ask whether we can use methods in global geometry to get results in contact topology. There is a notion of compatibility in this context which relates convexity concepts in those geometries and is well studied concerning geometry questions, but is not exploited for topological questions. I will talk about "contact sphere theorem" due to Etnyre-Massot-Komendarczyk, which might be the most interesting result for contact topologists.

A discussion on 3 dim Lens spaces.

Series
Geometry Topology Student Seminar
Time
Wednesday, March 7, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Atlanta
Speaker
Agniva RoyGaTech
Three dimensional lens spaces L(p,q) are well known as the first examples of 3-manifolds that were not known by their homology or fundamental group alone. The complete classification of L(p,q), upto homeomorphism, was an important result, the first proof of which was given by Reidemeister in the 1930s. In the 1980s, a more topological proof was given by Bonahon and Hodgson. This talk will discuss two equivalent definitions of Lens spaces, some of their well known properties, and then sketch the idea of Bonahon and Hodgson's proof. Time permitting, we shall also see Bonahon's result about the mapping class group of L(p,q).

Classification of knots in 3-sphere

Series
Geometry Topology Student Seminar
Time
Wednesday, February 28, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki MinGaTech
I will introduce the notion of satellite knots and show that a knot in a 3-sphere is either a torus knot, a satellite knot or a hyperbolic knot.

An introduction to the braid group.

Series
Geometry Topology Student Seminar
Time
Wednesday, February 21, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin KodrekGaTech
There are a number of ways to define the braid group. The traditional definition involves equivalence classes of braids, but it can also be defined in terms of mapping class groups, in terms of configuration spaces, or purely algebraically with an explicit presentation. My goal is to give an informal overview of this group and some of its subgroups, comparing and contrasting the various incarnations along the way.

Dehn surgery on the figure 8 knot

Series
Geometry Topology Student Seminar
Time
Wednesday, February 7, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki MinGaTech
The figure 8 knot is the simplest hyperbolic knot. In the late 1970s, Thurston studied how to construct hyperbolic manifolds from ideal tetrahedra. In this talk, I present the Thurston’s theory and apply this to the figure 8 knot. It turns out that every Dehn surgery on the figure 8 knot results in a hyperbolic manifold except for 10 exceptional surgery coefficients. If time permits, I will also introduce the classification of tight contact structures on these manifolds. This is a joint work with James Conway.

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 KolayGaTech
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 LanierGaTech
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 MukherjeeGeorgia 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.

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