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Wednesday, November 26, 2014 - 14:05 ,
Location: Skiles 006 ,
Eric Sabo ,
Georgia Institute of Technology ,
esabo3@gatech.edu ,
Organizer: Eric Sabo

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.

Wednesday, November 19, 2014 - 14:00 ,
Location: Skiles 006 ,
Elizabeth Bolduc ,
Georgia Tech ,
Organizer:

Wednesday, November 19, 2014 - 02:01 ,
Location: Skiles 006 ,
Elizabeth Bolduc ,
Georgia Tech ,
Organizer:

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!

Wednesday, November 12, 2014 - 14:00 ,
Location: Skiles 006 ,
Jamie Conway ,
Georgia Tech ,
Organizer: James Conway

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.

Wednesday, November 5, 2014 - 14:05 ,
Location: Skiles 006 ,
Shane Scott ,
GaTech ,
Organizer: Shane Scott

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.

Wednesday, October 29, 2014 - 14:00 ,
Location: Skiles 006 ,
Jonathan Paprocki ,
Georgia Tech ,
Organizer: Jonathan Paprocki

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.

Wednesday, October 22, 2014 - 14:00 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

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".

Wednesday, September 10, 2014 - 14:00 ,
Location: Skiles 006 ,
Jonathan Paprocki ,
Georgia Tech ,
Organizer: Jonathan Paprocki

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.

Wednesday, September 3, 2014 - 14:00 ,
Location: Skiles 006 ,
Jonathan Paprocki ,
Georgia Tech ,
Organizer: Jonathan Paprocki

Canceled due to speaker illness, date will be moved forward.