Virtual Seminar| Institute of Mathematical Sciences
Time：Thursday, January 7th, 14:00-15:00
Location：Room S501
Speaker: Sheng-Fu Chiu from Institute of Mathematics, Academia Sinica, Taipei
Title: Hamiltonian dynamics and symplectic rigidity from the viewpoint of dg-categories
Abstract: The famous Gromov-Eliashberg C^0-rigidity theorem is a miracle in symplectic geometry. Roughly speaking, the theorem asserts that the group of symplectomorphisms of a symplectic manifold is topologically closed in its group of diffeomorphisms, in the sense of uniform norm. It turns out that such rigidity has its roots deeply mined in the interaction between Hamiltonian dynamics and Poisson brackets under C^0-limit. Moreover, these functional analytical style properties are related to differential graded Hom structures of certain triangulated (or dg) categories. In this talk I will give an gentle introduction to Hamiltonian diffeomorphism groups and their Lie algebras, and explain how the homological idea of triangulated/dg categories can be used to answer these symplectic C^0-rigidity phenomena.