Seminars and Colloquia by Series

3-manifolds and lagrangian subspaces of character varieties

Series
Geometry Topology Seminar
Time
Monday, October 6, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
A. SikoraSUNY Buffalo
W. Goldman proved that the SL(2)-character variety X(F) of a closed surface F is a holonomic symplectic manifold. He also showed that the Sl(2)-characters of every 3-manifold with boundary F form an isotropic subspace of X(F). In fact, for all 3-manifolds whose SL(2)-representations are easy to analyze, these representations form a Lagrangian space. In this talk, we are going to construct explicit examples of 3-manifolds M bounding surfaces of arbitrary genus, whose spaces of SL(2)-characters have dimension as small as possible. We discuss relevance of this problem to quantum and classical low-dimensional topology.

Large N duality and integrable systems

Series
Geometry Topology Seminar
Time
Friday, October 3, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Tony PantevDept of Mathematics, University of Penn
I will describe a framework which relates large N duality to the geometry of degenerating Calabi-Yau spaces and the Hitchin integrable system. I will give a geometric interpretation of the Dijkgraaf-Vafa large N quantization procedure in this context.

Stable equivalence of manifolds

Series
Geometry Topology Seminar
Time
Monday, September 29, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Igor BelegradekSchool of Mathematics, Georgia Tech
This is an expository talk. A classical theorem of Mazur gives a simple criterion for two closed manifolds M, M' to become diffeomorphic after multiplying by the Euclidean n-space, where n large. In the talk I shall prove Mazur's theorem, and then discuss what happens when n is small and M, M' are 3-dimensional lens spaces. The talk shall be accessible to anybody with interest in geometry and topology.

Spectral invariants, the energy-capacity inequality, and the non-squeezing theorem

Series
Geometry Topology Seminar
Time
Monday, September 22, 2008 - 16:00 for 1 hour (actually 50 minutes)
Location
Room 322, Boyd Graduate Studies UGA
Speaker
Michael UsherDepartment of Mathematics, University of Georgia
Based on work of Schwarz and Oh, information coming from a filtration in Hamiltonian Floer homology can be used to construct "spectral invariants" for paths of Hamiltonian diffeomorphisms of symplectic manifolds. I will show how these invariants can be used to provide a unified approach to proving various old and new results in symplectic topology, including the non-degeneracy of the Hofer metric and some of its variants; a sharp version of an inequality between the Hofer-Zehnder capacity and the displacement energy; and a generalization of Gromov's non-squeezing theorem.

The HOMFLY polynomial, the trilogarithm and zeta(3)

Series
Geometry Topology Seminar
Time
Monday, September 22, 2008 - 14:30 for 2 hours
Location
Room 322, Boyd Graduate Studies UGA
Speaker
Stavros GaroufalidisSchool of Mathematics, Georgia Tech
I will discuss a relation between the HOMFLY polynomial of a knot, its extension for a closed 3-manifold, a special function, the trilogarithm, and zeta(3).  Technically, this means that we consider perturbative U(N) Chern-Simons theory around the trivial flat connection, for all N, in an ambient 3-manifold. This is rigorous, and joint with Marcos Marino and Thang Le.

Filling invariants for groups

Series
Geometry Topology Seminar
Time
Monday, September 15, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Pallavi DaniEmory University and LSU
The Dehn function of a finitely presented group measures the difficulty in filling loops in the presentation complex of the group. Higher dimensional Dehn functions are a natural generalization: the n-dimensional Dehn function of a group captures the difficulty of filling n-spheres with (n+1)-balls in suitably defined complexes associated with the group. A fundamental question in the area is that of determining which functions arise as Dehn functions. I will give an overview of known results and describe recent progress in the 2-dimensional case. This is joint work with Josh Barnard and Noel Brady.

The hyperbolic volume and Jones polynomial of an embedded graph

Series
Geometry Topology Seminar
Time
Monday, September 8, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Roland van der VeenUniversity of Amsterdam
The hyperbolic volume and the colored Jones polynomial are two of the most powerful invariants in knot theory. In this talk we aim to extend these invariants to arbitrary graphs embedded in 3-space. This provides new tools for studying questions about graph embedding and it also sheds some new light on the volume conjecture. According to this conjecture, the Jones polynomial and the volume of a knot are intimately related. In some special cases we will prove that this still holds true in the case of graphs.

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