Seminars and Colloquia by Series

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 PaprockiGeorgia 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 KolayGeorgia 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 PaprockiGeorgia 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.

Open book foliations.

Series
Geometry Topology Student Seminar
Time
Tuesday, June 24, 2014 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey KalotiGeorgia Tech.
We start studying open book foliations in this series of seminars. We will go through the theory and see how it is used in applications to contact topology.

Smooth infinitesimal analysis

Series
Geometry Topology Student Seminar
Time
Friday, May 2, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John DeverGeorgia Tech

Please Note: This is a final project for Dr. Etnyre's Differential Geometry class.

After briefly considering embeddings of the category of smooth manifolds into so called smooth toposes and arguing that we may ignore the details of the embedding and work from axioms if we agree to use intuitionistic logic, we consider axiomatic synthetic differential geometry. Key players are a space R playing the role of the "real line" and a space D consisting of null-square infinitesimals such that every function from D to R is "microlinear". We then define microlinear spaces and translate many definitions from differential geometry to this setting. As an illustration of the ideas, we prove Stokes' theorem. Time permitting, we show how synthetic differential geometry may be considered as an extension of differential geometry in that theorems proven in the synthetic setting may be "pulled back" to theorems about smooth manifolds.

Yamabe Problem.

Series
Geometry Topology Student Seminar
Time
Wednesday, April 30, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey KalotiGeorgia Tech.
Given a Riemannian manifold $(M,g)$, does there exist a metric $g'$ on $M$ conformal to $g$ such that $g'$ has constant scalar curvature? This question is known as the Yamabe problem. Aim of this talk is to give an overview of the problem and discuss and develop methods that go into solving a few of intermediate results in the solution to the problem in full generality.

Legendrian Torus Knots

Series
Geometry Topology Student Seminar
Time
Wednesday, April 23, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ece Gülşah ÇolakBülent Ecevit University and Georgia Tech
We will discuss Etnyre and Honda's proof of the classification of Legendrian positive torus knots in the tight contact 3-sphere up to Legendrian isotopy by using the tools from convex surface theory.

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