Seminars and Colloquia by Series

Introduction to the h-principle

Series
Geometry Topology Working Seminar
Time
Friday, January 23, 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.

Hyperbolic volume and torsions of 3-manifolds

Series
Geometry Topology Working Seminar
Time
Friday, November 14, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Thang Le – School of Mathematics, Georgia Tech
We will explain the famous result of Luck and Schick which says that for a large class of 3-manifolds, including all knot complements, the hyperbolic volume is equal to the l^2-torsion. Then we speculate about the growth of homology torsions of finite covers of knot complements. The talk will be elementary and should be accessible to those interested in geometry/topology.

On Sections of genus two Lefschetz fibrations

Series
Geometry Topology Working Seminar
Time
Friday, October 31, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Sinem Celik Onaran – School of Mathematics, Georgia Tech
It is still not known whether every genus g Lefschetz fibration over the 2-sphere admits a section or not. In this talk, we will give a brief background information on Lefschetz fibrations and talk about sections of genus two Lefschetz fibration. We will observe that any holomorphic genus two Lefschetz fibration without seperating singular fibers admits a section. This talk is accessible to anyone interested in topology and geometry.

Three closed, nonselfintersecting geodesics on the sphere

Series
Geometry Topology Working Seminar
Time
Friday, October 17, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jim Krysiak – School of Mathematics, Georgia Tech
This will be a continuation of the previous talk by this title. Specifically, this will be a presentation of the classical result on the existence of three closed nonselfintersecting geodesics on surfaces diffeomorphic to the sphere. It will be accessible to anyone interested in topology and geometry.

Three closed, nonselfintersecting geodesics on the sphere

Series
Geometry Topology Working Seminar
Time
Friday, September 26, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jim Krysiak – School of Mathematics, Georgia Tech
This will be a presentation of the classical result on the existence of three closed nonselfintersecting geodesics on surfaces diffeomorphic to the sphere. It will be accessible to anyone interested in topology and geometry.

Contact homology of Legendrian knots

Series
Geometry Topology Working Seminar
Time
Friday, September 19, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Etnyre – School of Mathematics, Georgia Tech
This will be an introduction to Legendrian knots (these are interesting knots that blend topological and geometric concepts) and a powerful invariant of Legendrian knots in R^3 called contact homology. On the first pass this invariant is combinatorial and has a lot of interesting algebraic structure. In a future talk (probably a few weeks from now), I will explain more about the analytic side of the theory as well as deeper algebraic aspects. This talk should be accessible anyone interested in topology and geometry.

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