How to count constant maps?

Geometry, Symmetry and Physics
Event time: 
Monday, December 2, 2019 - 4:00pm
LOM 214
Si Li
Speaker affiliation: 
Tsinghua University
Event description: 

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 mathematical 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, using Gauss-Manin connection. 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. 

Special note: 
Unusual time