Integrable systems and Hamiltonian flows in Calabi-Yau categories

Geometry, Symmetry and Physics
Event time: 
Monday, April 26, 2021 - 4:30pm
Location: (Password is the same as last semester)
Nick Rozenblyum
Speaker affiliation: 
University of Chicago
Event description: 

I will describe a general approach to constructing Hamiltonian
actions on moduli spaces from Calabi-Yau categories. In particular cases, this
specializes to give a "universal" Hitchin integrable system as well as the
Calogero-Moser system. Moreover, I will describe a generalization to higher
dimensions of a classical result of Goldman in geometric topology which says
that the Goldman Lie algebra of free loops on a surface acts by Hamiltonian
vector fields on the character variety of the surface. A key input is a
description of deformations of Calabi-Yau structures, which is of independent
interest. This is joint work with Chris Brav.