Venue: Quan 9, BICMR

Time: Monday, Mar. 23 , 13:00-15:00

Speaker: Si Li (Tsinghua University)

Abstract: Quantum field theory at one dimension (Quantum mechanics) leads to the beautiful notion of deformation quantization on Poisson manifold. The general deformation quantization is constructed by Kontsevich, however, by realizing the problem as the boundary theory of two dimensional Poisson sigma model. In this talk, I will describe a general structure of perturbative quantization for one dimensional Chern-Simons type theory. We show that it leads directly to a deformation quantization on symplectic manifold that is closely related to Fedosov's Abelian connection. As an application, I will show that the localization technique can be adapted to the perturbative renormalization which leads to a simple geometric proof of algebraic index theorem.