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Friday, November 4, 2011 - 14:05 ,
Location: Skiles 006 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

This is the first in the series of two talks aimed to discuss a recent work of Ontaneda which gives a poweful method of producing negatively curved manifolds. Ontaneda's work adds a lot of weight to the often quoted Gromov's prediction that in a sense most manifolds (of any dimension) are negatively curved.

Friday, October 21, 2011 - 14:00 ,
Location: Skiles 006 ,
Dan Margalit ,
GaTech ,
Organizer: Dan Margalit

I will discuss the Thurston norm for fibered hyperbolic 3-manifolds.

Friday, October 14, 2011 - 14:00 ,
Location: Skiles 006 ,
Mohammad Ghomi ,
Ga Tech ,
Organizer: John Etnyre

We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V>5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or points of vanishing torsion) of C. The proof, which employs curve shortening flow, is based on a corresponding inequality for the numbers of double points, singularites, and inflections of closed contractible curves in the real projective plane which intersect every closed geodesic. In the process we will also obtain some generalizations of classical theorems due to Mobius, Fenchel, and Segre (which includes Arnold's ``tennis ball theorem'').

Friday, October 7, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

Recall this is a 2 hour seminar.

This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Friday, September 30, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Recall this is a 2 hour seminar.

Friday, September 16, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Recall this is a 2 hour seminar (2-4).

Friday, September 9, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Recall this is a two hour seminar (2-4).

Friday, September 2, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Recall this is a two hour seminar (running from 2-4).

Friday, April 15, 2011 - 14:05 ,
Location: Skiles 269 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

A basic metric invariant of an open complete nonnegatively curved manifold is the isometry type of its soul. In the talk I shall discuss whether the soul depends continuously on the metric.

Friday, April 8, 2011 - 14:05 ,
Location: Skiles 269 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

I will prove contractibility of the space of nonnegatively curved metrics on the 2-sphere via the uniformization, discuss difficulties of extending the result to metrics on the plane, and then discuss similar problems in higher dimensions.