Seminars and Colloquia by Series

Monday, March 25, 2013 - 14:00 , Location: Skiles 006 , I. Dynnikov , Moscow State University , Organizer: Thang Le
A few years ago I proved that any rectangular diagram of the unknot admits monotonic simplification by elementary moves. More recently M.Prasolov and I addressed the question: when a rectangular diagram of a link admits at least one step of simplification? It turned out that an answer can be given naturally in terms of Legendrian links. On this way, we resolved positively a conjecture by V.Jones on the invariance of the algebraic crossing number of a minimal braid, and a few similar questions.
Tuesday, March 19, 2013 - 15:05 , Location: Skiles 006 , Christian Zickert , University of Maryland , , Organizer: Stavros Garoufalidis
 Thurston's gluing equations are polynomial equations invented byThurston to explicitly compute hyperbolic structures or, more generally, representations in PGL(2,C). This is done via so called shape coordinates.We generalize the shape coordinates to obtain a parametrization ofrepresentations in PGL(n,C). We give applications to quantum topology, anddiscuss an intriguing duality between the shape coordinates and thePtolemy coordinates of Garoufalidis-Thurston-Zickert. The shapecoordinates and Ptolemy coordinates can be viewed as 3-dimensional analogues of the X- and A-coordinates on higher Teichmuller spaces due toFock and Goncharov.
Monday, March 18, 2013 - 18:39 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Monday, March 11, 2013 - 14:00 , Location: Skiles 006 , Jamie Conway , Georgia Tech , Organizer: James Conway

Note: this is a 40 minute talk.

We will explore the notion of surgery on transverse knots in contact 3-manifolds.  We will see situations when this operation does or does not preserves properties of the original contact structure, and avenues for further research.
Monday, February 4, 2013 - 14:00 , Location: Skiles 006 , Russell Avdek , USC , Organizer: John Etnyre
We introduce a new surgery operation for contact manifolds called the Liouville connect sum.  This operation -- which includes Weinstein handle attachment as a special case -- is designed to study the relationship between contact topology and symplectomorphism groups established by work of Giroux and Thurston-Winkelnkemper.  The Liouville connect sum is used to generalize results of Baker-Etnyre-Van Horn-Morris and Baldwin on the existence of "monodromy multiplication cobordisms" as well as results of Seidel regarding squares of symplectic Dehn twists.
Monday, January 28, 2013 - 14:00 , Location: Skiles 006 , Adam Knapp , Columbia University , Organizer: John Etnyre
Given any smooth manifold, there is a canonical symplectic structure on its cotangent bundle. A long standing idea of Arnol'd suggests that the symplectic topology of the cotangent bundle should contain a great deal of information about the smooth topology of its base. As a contrast, I show that when X is an open 4-manifold, this symplectic structure on T^*X does not depend on the choice of smooth structure on X. I will also discuss the particular cases of smooth structures on R^4 and once-punctured compact 4-manifolds.
Monday, January 21, 2013 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Monday, January 14, 2013 - 14:05 , Location: Skiles 006 , Dan Margalit , Georgia Institute of Technology , Organizer: Dan Margalit
We give a simple generating set for the following three closely related groups: the hypereliptic Torelli group, the kernel of the integral Burau representation, and the fundamental group of the branch locus of the period mapping.  Our theorem confirms a conjecture of Hain.  This is joint work with Tara Brendle and Andy Putman.
Monday, December 10, 2012 - 14:05 , Location: Skiles 006 , Stavros Garoufalidis , Georgia Tech , , Organizer: Stavros Garoufalidis
I will explain how to construct a 4-variable knot invariant which expresses a recursion for the colored HOMFLY polynomial of a knot, and its implications on (a) asymptotics (b) the SL2 character variety of the knot (c) mirror symmetry.
Monday, November 26, 2012 - 14:00 , Location: Skiles 006 , Ali Maalaoui , Rutgers University , Organizer: John Etnyre
In this talk we are going to present a theorem that can be seen as related to S. Smale's theorem on the topology of the space of Legendrian loops. The framework will be slightly different and the space of Legendrian curves will be replaced by a smaller space $C_{\beta}$, that appears to be convenient in some variational problems in contact form geometry. We will also talk about the applications and the possible extensions of this result. This is a joint work with V. Martino.