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.