Geometry & Topology Seminar

Shifted Poisson structure and elliptic deformation

About the speaker:

Dr. Zheng Hua(华诤) is assistant Professor at the University of Hong Kong. He obtained his Ph.D. from University of Wisconsin, Madison in 2009. His research field is Algebraic geometry and he currently focuses on Donaldson-Thomas theory, Derived category and Moduli space of sheaves.

Abstract:

In their seminal paper, Pantev, Toen, Vaquie and Vezzosi introduced the notion of shifted symplectic structure on derived stacks. Later PTVV+Calaque further introduced the shifted Poisson structure. In this talk, I will present my recent work joint with Alexander Polishchuk. We prove that the moduli space of complexes of vector bundles (up to chain isomorphisms) on CY d-fold carries a (1-d)-shifted Poisson structure. This generalises various interesting Poisson structures in algebraic geometry and integrable systems. Finally, I will explain how to use our theorem to classify the symplectic leaves of elliptic loop algebra with the Poisson structure defined by the elliptic solution of the classical Yang-Baxter equation.