Title: How to count constant maps?
Speaker: Si Li
Speaker Info: Tsinghua University
The art of using quantum field theory to derive mathematical results often lies in a mysterious transition between infinite dimensional geometry and finite dimensional geometry. In this talk we describe a general framework to study the quantum geometry of $\sigma$-models when they are effectively localized to small fluctuations around constant maps. We illustrate how to turn the physics idea of exact semi-classical approximation into a geometric set-up in this framework. This leads to a theory of “counting constant maps” in a nontrivial way. We explain this program by a concrete example of topological quantum mechanics and show how “counting constant loops” leads to a simple proof of the algebraic index theorem using Getzler’s Gauss-Manin connection.Date: Friday, December 6, 2019