Seminars and Colloquia by Series

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 BelegradekGa 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 BelegradekGa 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 BelegradekSchool 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 GhomiSchool 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 GhomiGa 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.)

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 GhomiGa 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 LeSchool 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 OnaranSchool 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 KrysiakSchool 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 KrysiakSchool 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.

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