EVENT DETAILS AND ABSTRACT

Title: Deformations of Calabi-Yau categories and Poisson structures
Speaker: Nick Rozenblyum
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

I will describe a correspondence between algebraic structures on DG categories and geometric structures on corresponding moduli spaces. This correspondence is given by deformation theory and provides a uniform conceptual approach to many structures on Hochschild type invariants. In particular, I will explain how DG categories with pre-Calabi-Yau structure, in the sense of Kontsevich-Vlassopoulos, are noncommutative analogs of log Calabi-Yau varieties, and show that such structures induce Poisson structures on corresponding moduli spaces, generalizing a result of Yeung. In particular, this recovers standard examples of Poisson structures on moduli spaces of sheaves on del Pezzo surfaces, generalizations to higher dimensional Fano varieties, and more exotic examples coming from higher genus curves and non-commutative algebras. This is joint work with Chris Brav.