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

来源：数学科学学院发布时间：2023-03-29 150

代数几何与辛几何系列学术报告

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

报告人：吴惟为（浙江大学数学学院长聘副教授）

时间：2023年4月6日星期四下午2:45-3:45

地点：浙大紫金港校区海纳苑2幢210

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