Integrable systems from Calabi-Yau categories

Abstract: I will describe a general categorical approach to constructing Hamiltonian actions on moduli spaces. 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 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.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar