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Friday, June 22, 2012 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

There is little known about the existence of contact strucutres in high dimensions, but recently in work of Casals, Pancholi and Presas the 5 dimensional case is largely understood. In this talk I will discuss the existence of contact structures on 5-manifold and outline an alternate construction that will hopefully prove that any almost contact structure on a 5-manifold is homotopic, though almost contact structures, to a contact structure.

Friday, April 13, 2012 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

Note this is a 2 hour talk.

In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Friday, April 6, 2012 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Note this is a 2 hour talk.

Friday, March 30, 2012 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Note this is a 2 hour talk

Friday, November 11, 2011 - 14:05 ,
Location: Skiles 006 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

This is the second 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. In the second talk I shall discuss some ideas of the proof.

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.