Mapping class groups in symplectic geometry: from packing problem to moduli spaces

Title: Mapping class groups in symplectic geometry: from packing problem to moduli spaces

Speaker: Wu weiwei(Tenured Associate Professor of School of Mathematical Sciences, Zhejiang University)

Time: 2023-04-06, 15:00-16:00

Location: 210, Building 2, Hainayuan, School of Mathematical Science, Zijingang Campus

Abstract: Symplectic packing problem  is one of the central theme in symplectic geometry, after Gromov’s celebrating non-squeezing theorem.  Many works have been done to study whether a symplectic region can be packed into a given symplectic manifold.  

We take a different perspective and relate the topology of the space of symplectic packing to the mapping class group of the blown-up manifold.  It turns out to be related to a class of symplectic automorphism called the “ball-swapping”.  Furthermore, we relate the story to the monodromy problem in algebraic geometry, and another more classical symplectic automorphism called “Dehn twists”.  This leads to applications to uniqueness theorems of Lagrangian embeddings, classifications of homotopy types of symplectic automorphism groups and classification of finite group actions