## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** How to count constant maps?

**Speaker:** Si Li

**Speaker Info:** Tsinghua University

**Brief Description:**

**Special Note**:

**Abstract:**

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

**Time:** 11am

**Where:** Lunt 107

**Contact Person:** Ezra Getzler

**Contact email:** getzler@northwestern.edu

**Contact Phone:**

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