Seminars and Colloquia by Series

Integral homology of hyperbolic three--manifolds

Series
Geometry Topology Seminar
Time
Friday, April 5, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jean Raimbault – Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie
It is a natural question to ask whether one can deduce topological properties of a finite--volume three--manifold from its Riemannian invariants such as volume and systole. In all generality this is impossible, for example a given manifold has sequences of finite covers with either linear or sub-linear growth. However under a geometric assumption, which is satisfied for example by some naturally defined sequences of arithmetic manifolds, one can prove results on the asymptotics of the first integral homology. I will try to explain these results in the compact case (this is part of a joint work with M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov and I. Samet) and time permitting I will discuss their extension to manifolds with cusps such as hyperbolic knot complements.

Acylindrically hyperbolic groups

Series
Geometry Topology Seminar
Time
Monday, April 1, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Denis Osin – Vanderbilt
A group is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. This class encompasses many examples of interest: hyperbolic and relatively hyperbolic groups, Out(F_n) for n>1, all but finitely many mapping class groups, most fundamental groups of 3-manifolds, groups acting properly on proper CAT(0) spaces and containing rank 1 elements, 1-relator groups with at least 3 generators, etc. On the other hand, many results known for these particular classes can be naturally generalized in the context of acylindrically hyperbolic groups. In my talk I will survey some recent progress in this direction. The talk is partially based on my joint papers with F. Dahmani, V. Guirardel, M.Hull, and A. Minasyan.

Monotonic simplification of rectangular diagrams and contact topology

Series
Geometry Topology Seminar
Time
Monday, March 25, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
I. Dynnikov – Moscow State University
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.

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.

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