Seminars and Colloquia by Series

Series

Introduction to Bordered Heegaard-Floer homology II

Series: Geometry Topology Working Seminar
Time: Wednesday, October 28, 2009 - 10:00 for 1.5 hours (actually 80 minutes)
Location: Skiles 255
Speaker: Shea Vela-Vick – Columbia University

Here we will introduce the basic definitions of bordered Floer homology. We will discuss bordered Heegaard diagrams as well as the algebraic objects, like A_\infinity algebras and modules, involved in the theory. We will also discuss the pairing theorem which states that if Y = Y_1 U_\phi Y_2 is obtained by identifying the (connected) boundaries of Y_1 and Y_2, then the closed Heegaard Floer theory of Y can be obtained as a suitable tensor product of the bordered theories of Y_1 and Y_2.Note the different time and place!This is a 1.5 hour talk.

Introduction to Bordered Heegaard-Floer homology

Series: Geometry Topology Working Seminar
Time: Monday, October 26, 2009 - 10:00 for 1.5 hours (actually 80 minutes)
Location: Skiles 255
Speaker: Shea Vela-Vick – Columbia University

We will focus on the "toy model" of bordered Floer homology. Loosely speaking, this is bordered Floer homology for grid diagrams of knots. While the toy model unfortunately does not provide us with any knot invariants, it highlights many of the key ideas needed to understand the more general theory. Note the different time and place! This is a 1.5 hour talk.

Introduction to Heegaard Floer Homology

Series: Geometry Topology Working Seminar
Time: Friday, October 23, 2009 - 15:00 for 2 hours
Location: Skiles 269
Speaker: Amey Kaloti – Georgia Tech

Please Note: This is a 2 hour talk.

Abstract: Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with connections to contact topology. In these talks we will try to define the Heegaard Floer homology without assuming much background in low dimensional topology. One more goal is to present the combinatorial description for this theory.

Introduction to Heegaard Floer Homology

Series: Geometry Topology Working Seminar
Time: Friday, October 16, 2009 - 15:00 for 2 hours
Location: Skiles 169
Speaker: Amey Kaloti – Georgia Tech

Please Note: This is a 2-hour talk.

Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with connections to contact topology. In these talks we will try to define the Heegaard Floer homology without assuming much background in low dimensional topology. One more goal is to present the combinatorial description for this theory.

On classification of of high-dimensional manifolds-II

Series: Geometry Topology Working Seminar
Time: Friday, October 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location: Skiles 269
Speaker: Igor Belegradek – Georgia Tech

This 2 hour talk is a gentle introduction to simply-connected sugery theory (following classical work by Browder, Novikov, and Wall). The emphasis will be on classification of high-dimensional manifolds and understanding concrete examples.

On classification of of high-dimensional manifolds

Series: Geometry Topology Working Seminar
Time: Friday, October 2, 2009 - 15:00 for 2 hours
Location: Skiles 269
Speaker: Igor Belegradek – Georgia Tech

Introduction to Contact Homology

Series: Geometry Topology Working Seminar
Time: Friday, September 25, 2009 - 15:00 for 2 hours
Location: Skiles 269
Speaker: Anh Tran – Georgia Tech

Please Note: (This is a 2 hour lecture.)

In this talk I will give a quick review of classical invariants of Legendrian knots in a 3-dimensional contact manifold (the topological knot type, the Thurston-Bennequin invariant and the rotation number). These classical invariants do not completely determine the Legendrian isotopy type of Legendrian knots, therefore we will consider Contact homology (aka Chekanov-Eliashberg DGA), a new invariant that has been defined in recent years. We also discuss the linearization of Contact homology, a method to extract a more computable invariant out of the DGA associated to a Legendrian knot.

Hyperbolic structures on surfaces and 3-manifolds

Series: Geometry Topology Working Seminar
Time: Friday, September 18, 2009 - 14:00 for 1.5 hours (actually 80 minutes)
Location: Skiles 269
Speaker: John Etnyre – Georgia Tech

We will discuss how to put a hyperbolic structure on various surface and 3-manifolds. We will being by discussing isometries of hyperbolic space in dimension 2 and 3. Using our understanding of these isometries we will explicitly construct hyperbolic structures on all close surfaces of genus greater than one and a complete finite volume hyperbolic structure on the punctured torus. We will then consider the three dimensional case where we will concentrate on putting hyperbolic structures on knot complements. (Note: this is a 1.5 hr lecture)

Hyperbolic structures on surfaces and 3-manifolds

Series: Geometry Topology Working Seminar
Time: Friday, September 11, 2009 - 15:00 for 2 hours
Location: Skiles 269
Speaker: John Etnyre – Georgia Tech

The Jones polynomial and quantum invariants

Series: Geometry Topology Working Seminar
Time: Friday, April 24, 2009 - 15:00 for 2 hours
Location: Skiles 269
Speaker: Thang Le – School of Mathematics, Georgia Tech

Please Note: These are two hour lectures.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.

Georgia Institute of Technology College of Sciences

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