Seminars and Colloquia by Series

Thurston's gluing equations for PGL(n,C)

Series
Geometry Topology Seminar
Time
Tuesday, March 19, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian Zickert – University of Maryland –
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.

Oral Exam: Transverse Surgery in Contact Manifolds

Series
Geometry Topology Seminar
Time
Monday, March 11, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech

Please Note: 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.

The Liouville connect sum and its applications

Series
Geometry Topology Seminar
Time
Monday, February 4, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Russell Avdek – USC
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.

Symplectic structures on cotangent bundles of open 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, January 28, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Adam Knapp – Columbia University
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.

Generators for the hyperelliptoc Torelli group and the kernel of the integral Burau representation

Series
Geometry Topology Seminar
Time
Monday, January 14, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Institute of Technology
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.

The colored HOMFLY polynomial is q-holonomic

Series
Geometry Topology Seminar
Time
Monday, December 10, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stavros Garoufalidis – Georgia Tech –
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.

The topology of a subspace of the Legendrian curves in a closed contact 3-manifold

Series
Geometry Topology Seminar
Time
Monday, November 26, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ali Maalaoui – Rutgers University
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.

Near-symplectic 6-manifolds with PS-overtwisted contact submanifolds

Series
Geometry Topology Seminar
Time
Monday, November 19, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ramon Vera – Durham University
We discuss two concepts of low-dimensional topology in higher dimensions: near-symplectic manifolds and overtwisted contact structures. We present a generalization of near-symplectic 4-manifolds to dimension 6. By near-symplectic, we understand a closed 2-form that is symplectic outside a small submanifold where it degenerates. This approach uses some singular mappings called generalized broken Lefschetz fibrations. An application of this setting appears in contact topology. We find that a contact 5-manifold, which appears naturally in this context, is PS-overtwisted. This property can be detected in a rather simple way.

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