Seminars and Colloquia by Series

The boundary of the curve complex

Series
Geometry Topology Student Seminar
Time
Wednesday, December 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Krone – Georgia Tech
I will present a result of Klarreich on the boundary at infinity of the complex of curves of a compact orientable surface. The complex of curves is a delta-hyperbolic space so it has a boundary which is the set of equivalence classes of quasi-geodesic rays. Klarreich shows that the resulting space is homeomorphic to the space of minimal foliations of the surface.

Alexander's Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 26, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric Sabo – Georgia Institute of Technology –

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

I will present a modern proof of Alexander's Theorem using Morse Theory and surgery.

Dehn-Nielsen-Baer Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 19, 2014 - 02:01 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Elizabeth Bolduc – Georgia Tech
The Dehn Nielsen Baer Theorem states that the extended mapping class group is isomorphic to the outer automorphisms of π1(Sg). The theorem highlights the connection between the topological invariant of distinct symmetries of a space and its fundamental group. This talk will incorporate ideas from algebra, topology, and hyperbolic geometry!

Fenchel-Nielsen Coordinates on Teichmüller Space

Series
Geometry Topology Student Seminar
Time
Wednesday, November 12, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech
A surface with negative Euler characteristic has a hyperbolic metric. However, this metric is not unique. We will consider the Teichmüller space of a surface, which is the space of hyperbolic structures up to an equivalence relation. We will discuss the topology of and how to put coordinates on this space. If there is time, we will see that the lengths of 9g-9 curves determine the hyperbolic structure.

The Thurston Norm

Series
Geometry Topology Student Seminar
Time
Wednesday, November 5, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shane Scott – GaTech
The genus of a knot can be thought of as a measure of complexity for a 3 dimensional knot compliment. This notion can be extended to compact 3 manifolds by defining a norm on the second homology group with real coefficients measuring the Euler characteristic of embedded surfaces.

The Colored Jones Polynomial and the Volume Conjecture

Series
Geometry Topology Student Seminar
Time
Wednesday, October 29, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Paprocki – Georgia Tech

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

We will present an introduction to the notion of quantum invariants of knots and links, and in particular the colored Jones polynomial. We will also introduce the Volume Conjecture, which relates a certain limiting behavior of a quantum invariant (the colored Jones polynomial of a link) with a classical invariant (the hyperbolic volume of the hyperbolic part of a link complement in S^3) and has been proven in a number of cases.

The Loop Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, October 22, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

In this talk we will discuss the Loop Theorem, which is a generalization of Dehn's lemma. We will outline a proof using the "tower construction".

Chern-Simons theory and knot invariants

Series
Geometry Topology Student Seminar
Time
Wednesday, September 10, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Paprocki – Georgia Tech
We will present an introduction to gauge theory and classical Chern-Simons theory, a 3-dimensional topological gauge field theory whose quantization yields new insights about knot invariants such as the Jones polynomial. Then we will give a sketch of quantum Chern-Simons theory and how Witten used it as a 3-dimensional method to obtain the Jones polynomial, as well as how it may be used to obtain other powerful knot and 3-manifold invariants. No physics background is necessary.

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