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Friday, September 2, 2011 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

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

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, 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.

Friday, April 1, 2011 - 14:05 ,
Location: Skiles 269 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

The talk will be about my ongoing work on spaces of complete non-negatively curved metrics on low-dimensional manifolds, such as Euclidean plane, 2-sphere, or their product.

Friday, March 4, 2011 - 14:00 ,
Location: Skiles 269 ,
Taylor McNeill ,
Rice University ,
Organizer: John Etnyre

While orientable surfaces have been classified, the structure of their homeomorphism groups is not well understood. I will give a short introduction to mapping class groups, including a description of a crucial representation for these groups, the Magnus representation. In addition I will talk about some current work in which I use Johnson-type homomorphisms to define an infinite filtration of the kernel of the Magnus representation.

Friday, February 25, 2011 - 14:00 ,
Location: Skiles 269 ,
Mohammad Ghomi ,
Ga Tech ,
Organizer: John Etnyre

Torsion of a curve in Euclidean 3-space is a quantity which together with the curvature completely determines the curve up to a rigid motion. In this talk we use the curve shortening flow to show that the number of zero torsion points (or vertices) v a closed space curve c and the number p of the pair of parallel tangent lines of c satisfy the following sharp inequality: v + 2p > 5.

Friday, February 25, 2011 - 14:00 ,
Location: Skiles 269 ,
Dan Margalit ,
GaTech ,
Organizer: Dan Margalit

I'll present a new, simple proof that the Torelli group is generated by (infinitely many) bounding pair maps. At the end, I'll explain an application of this approach to the hyperelliptic Torelli group. The key is to take advantage of the "complex of minimizing cycles."

Friday, February 11, 2011 - 14:00 ,
Location: Skiles 269 ,
John Etnyre ,
School of Mathematics, Georgia Tech ,
Organizer: John Etnyre

This is part two of a lecture series investigating questions in contact geometry from the perspective of Riemannian geometry. Interesting questions in Riemannian geometry arising from contact geometry have a long and rich history, but there have been few applications of Riemannian geometry to contact topology. In these talks I will discuss basic connections between Riemannian and contact geometry and some applications of these connections. I will also discuss the "contact sphere theorem" that Rafal Komendarczyk, Patrick Massot and I recently proved as well as other results.

Friday, February 4, 2011 - 14:00 ,
Location: Skiles 269 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

This will be the first of a two part lecture series investigating questions in contact geometry from the perspective of Riemannian geometry. Interesting questions in Riemannian geometry arising from contact geometry have a long and rich history, but there have been few applications of Riemannian geometry to contact topology. In these talks I will discuss basic connections between Riemannian and contact geometry and some applications of these connections. I will also discuss the "contact sphere theorem" that Rafal Komendarczyk, Patrick Massot and I recently proved as well as other results.