Integrability Seminar: Rinat Kashaev, University of Geneva

Rinat Kashaev, University of Geneva

Title: State Integrals of Turaev-Viro Type on Shaped Triangulations
Program: Integrability in Modern Theoretical and Mathematical Physics
Speaker: Rinat Kashaev, University of Geneva
Date: Thursday, December 20, 2012
Time: 2:30pm – 3:30pm
Place: Seminar Room 313, Simons Center




: A shaped triangulation is a triangulation of an oriented pseudo 3-manifold where each tetrahedron carries dihedral angles of an ideal hyperbolic tetrahedron. For a given shaped triangulation, one can associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3-2 Pachner moves and the shape gauge transformations generated by the total dihedral angles around internal edges through the Neumann-Zagier Poisson bracket. Similarly to Turaev-Viro theory, the state variables live on edges of the triangulation but take their values on the
whole real axis. The tetrahedral weight functions enjoy a manifest tetrahedral symmetry and they are given in terms of a quantized beta-function. At least for shaped triangulations of closed 3-manifolds, up to normalization, this partition function is conjectured to be the absolute value squared of the partition function of the Teichmüller TQFT. This is similar to the known relationship between the Turaev-Viro and the Witten-Reshetikhin-Turaev invariants of three manifolds. The talk is based on the joint work with Feng Luo and Grigory Vartanov arXiv:1210.8393.