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Monday, January 31, 2022
4:00 PM - 5:00 PM
Online Event

Algebra and Geometry Seminar

Hamiltonian flows in Calabi-Yau categories
Nick Rozenblyum, Department of Mathematics, University of Chicago,

A classical result of Goldman states that the character variety of an oriented surface is a symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of this result in the setting of noncommutative Calabi-Yau geometry. One incarnation of this result is a higher-dimensional version of Goldman's theorem: the Chas-Sullivan string Lie algebra acts on by Hamiltonian vector fields on the (derived) character stack of a closed oriented manifold. Other incarnations include Hitchin's integrable system and the action of the necklace Lie algebra on Nakajima quiver stacks. This is joint work with Christopher Brav.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.