Algebra and Geometry Seminar

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.