Friday, October 3, 2008 - 14:00 , Location: Skiles 269 , Tony Pantev , Dept of Mathematics, University of Penn , Organizer: Stavros Garoufalidis
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.
Monday, September 29, 2008 - 14:00 , Location: Skiles 269 , Igor Belegradek , School of Mathematics, Georgia Tech , Organizer: Igor Belegradek
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.
Monday, September 22, 2008 - 16:00 , Location: Room 322, Boyd Graduate Studies UGA , Michael Usher , Department of Mathematics, University of Georgia , Organizer: John Etnyre
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.
Monday, September 22, 2008 - 14:30 , Location: Room 322, Boyd Graduate Studies UGA , Stavros Garoufalidis , School of Mathematics, Georgia Tech , Organizer: John Etnyre
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.
Monday, September 15, 2008 - 14:00 , Location: Skiles 269 , Pallavi Dani , Emory University and LSU , Organizer: John Etnyre
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.
Monday, September 8, 2008 - 14:00 , Location: Skiles 269 , Roland van der Veen , University of Amsterdam , Organizer: Stavros Garoufalidis
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.