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Friday, January 18, 2013 - 11:30 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre

This is the first of 4 or 5, 1.5 hour talks.

In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Friday, November 2, 2012 - 13:00 ,
Location: Skiles 006 ,
Various ,
Ga Tech ,
Organizer: John Etnyre

Friday, October 5, 2012 - 13:05 ,
Location: Skiles 006 ,
Igor Belegradek ,
Georgia Tech ,
Organizer: Igor Belegradek

The talk will be about manifolds covered by the Euclidean space yet admitting no complete metric of nonpositive curvature.

Friday, September 21, 2012 - 13:05 ,
Location: Skiles 006 ,
Mohammad Ghomi ,
Georgia Tech ,
ghomi@math.gatech.edu ,
Organizer: Mohammad Ghomi

A well-known problem in discerte convex geometry, attributed to the Dutch painter Durrer and first formulated by G. C. Shephard, is concerned with whether every convex polyope P in Euclidean 3-space has a simpe net, i.e., whether the surface of P can be isometrically embedded in the Euclidean plane after it has been cut along some spanning tree of its edges. In this talk we show that the answer is yes after an affine transformation. In particular the combinatorial structure of P plays no role in deciding its unfoldability, which settles a question of Croft, Falconer, and Guy. The proof employs a topological lemma which provides a criterion for checking embeddedness of immersed disks.

Friday, September 14, 2012 - 13:05 ,
Location: Skiles 006 ,
Dan Margalit ,
GaTech ,
Organizer: Dan Margalit

We will introduce characteristic classes of surface bundles over surfaces. This will be a slower version of a talk I gave over the summer. The goal is to get to some of the recent papers on the subject.

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.