Title: Eigenfunctions on a Riemannian manifold and representations of a vertex operator algebra

Time: Thursday January 5, 2012, 15:00-17:00 pm

Speaker: Professor Yi-Zhi Huang (Rutgers University and Peking University)

Abstract: Conjectures by physicists on nonlinear sigma models are one of the most influential sources of inspirations and motivations for many works in geometry in the past two or three decades. Unfortunately nonlinear sigma models are still not mathematically constructed. In this talk, I will discuss the first step in a program to construct these models mathematically using Riemannian geometry and the representation theory of vertex operator algebras. Given a Riemannian manifold M, for certain sufficiently small open neighborhood of a point on M, using normal coordinates at points in the neighborhood, we construct a module for a Heisenberg algebra generated by the space of smooth functions. Using certain submodules of these modules and the gluing method, we construct a sheaf of weak modules for a sheaf of vertex operator algebras generated by the sheaf of smooth functions. In particular, we construct an L(0)-semisimple lower-bounded generalized module for the vertex operator algebra of global sections on M generated by an eigenfunction of the Laplacian on M.

Venue: Room 09 at Quan-Zhai ( 全斋), New location for BICMR, Peking University