Seminars and Colloquia by Series

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
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 2 hr seminar)

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.

The Jones polynomial and quantum invariants

Series
Geometry Topology Working Seminar
Time
Friday, April 17, 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.

The Jones polynomial and quantum invariants

Series
Geometry Topology Working Seminar
Time
Friday, April 10, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Thang Le – School of Mathematics, Georgia Tech

Please Note: These are two hour talks.

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.

Introduction to metric and comparison geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 27, 2009 - 15:05 for 2.5 hours
Location
Skiles 269
Speaker
Igor Belegradek – Ga Tech
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the third (2 hour) lecture I shall prove volume and Laplacian comparison theorems.

Introduction to metric and comparison geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 20, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Igor Belegradek – Ga Tech
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics.

Introduction to metric and comparison geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Igor Belegradek – School of Mathematics, Georgia Tech
Comparison geometry studies Riemannian manifolds with a given curvature bound.  This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the first (2 hour) lecture I shall explain what volume comparison is and derive several applications.

Introduction to the h-principle

Series
Geometry Topology Working Seminar
Time
Friday, February 6, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Mohammad Ghomi – School of Mathematics, Georgia Tech

Please Note: (Please note this course runs from 3-5 pm.)

h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

Introduction to the h-principle

Series
Geometry Topology Working Seminar
Time
Friday, January 30, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Mohammad Ghomi – Ga Tech
$h$-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the $C^1$ isometric embedding theorem of Nash. (Please note this course runs from 3-5.)

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