Seminars and Colloquia by Series

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 Min – GaTech
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 Kodrek – GaTech
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 Min – GaTech
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 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.

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