Venue: Lecture Hall of IASM

Time: 10:30 - 11:50, January 12

Speaker: 刘思阳 Si-Yang Liu (University of Bonn)

Pretalk: Categorification of Fixed Points

Abstract: One important goal of classical mechanics is to understand periodic orbits of motions of particles. Via Hamiltonian formalism, this can be rephrased as fixed points of certain self-diffeomorphisms of a given manifold. There are conjectures relating such fixed points to the topology of spaces, which were resolved via “categorifying fixed points.”

Research talk: Symplectic Geometry of Degenerations

Abstract: Degeneration of algebraic varieties is a classical but powerful way of studying algebraic and symplectic geometry. While algebraic structures vary in a family, their de Rham cohomologies remain locally constant, leading to Schmid’s construction of mixed Hodge structures that essentially describes the geometry of the degenerate variety. Symplectic structures behave similarly, and one expects a parallel localization formula relating the symplectic geometry of a smooth fiber to that of a degenerate fiber. In this talk, I will discuss a special case where this philosophy can be translated into concrete statements and some applications. This is based on joint work in preparation with Sheel Ganatra, Wenyuan Li, and Peng Zhou.