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Friday, February 13, 2009 - 15:00 ,
Location: Skiles 269 ,
Igor Belegradek ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

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.

Friday, February 6, 2009 - 15:00 ,
Location: Skiles 269 ,
Mohammad Ghomi ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

<p>(Please note this course runs from 3-5 pm.)</p>

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.

Friday, January 30, 2009 - 15:00 ,
Location: Skiles 269 ,
Mohammad Ghomi ,
Ga Tech ,
Organizer: John Etnyre

$h$-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.)

Friday, January 23, 2009 - 15:00 ,
Location: Skiles 269 ,
Mohammad Ghomi ,
Ga Tech ,
Organizer: John Etnyre

$h$-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.

Friday, November 14, 2008 - 14:00 ,
Location: Skiles 269 ,
Thang Le ,
School of Mathematics, Georgia Tech ,
Organizer: Thang Le

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.

Friday, October 31, 2008 - 14:00 ,
Location: Skiles 269 ,
Sinem Celik Onaran ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

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.

Friday, October 17, 2008 - 14:00 ,
Location: Skiles 269 ,
Jim Krysiak ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

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.

Friday, September 26, 2008 - 14:00 ,
Location: Skiles 269 ,
Jim Krysiak ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

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.

Friday, September 19, 2008 - 14:00 ,
Location: Skiles 269 ,
John Etnyre ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

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.

Friday, September 12, 2008 - 14:00 ,
Location: Skiles 269 ,
Stavros Garoufalidis ,
School of Mathematics, Georgia Tech ,
Organizer: Stavros Garoufalidis

We will discuss, with examples, the Jones polynomial of the two simplest knots (the trefoil and the figure eight) and its loop expansion.