Seminars and Colloquia by Series

Tangent lines, inflection points, and vertices of closed space curves

Series
Geometry Topology Working Seminar
Time
Friday, October 14, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
Mohammad Ghomi – Ga Tech
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'').

Holomorphic curves in geometry and topology V

Series
Geometry Topology Working Seminar
Time
Friday, October 7, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: 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).

Holomorphic curves in geometry and topology IV

Series
Geometry Topology Working Seminar
Time
Friday, September 30, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: 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).

Holomorphic curves in geometry and topology III

Series
Geometry Topology Working Seminar
Time
Friday, September 16, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Recall this is a 2 hour seminar (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).

Holomorphic curves in geometry and topology II

Series
Geometry Topology Working Seminar
Time
Friday, September 9, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Recall this is a two hour seminar (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).

Holomorphic curves in geometry and topology

Series
Geometry Topology Working Seminar
Time
Friday, September 2, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: 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).

Spaces of nonnegatively curved metrics II

Series
Geometry Topology Working Seminar
Time
Friday, April 8, 2011 - 14:05 for 2 hours
Location
Skiles 269
Speaker
Igor Belegradek – Georgia Tech
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.

Spaces of nonnegatively curved metrics

Series
Geometry Topology Working Seminar
Time
Friday, April 1, 2011 - 14:05 for 2 hours
Location
Skiles 269
Speaker
Igor Belegradek – Georgia Tech
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.

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