Venue: Room 204, Hai Na Yuan #2, Zijingang Campus

Time: 16:00-17:20, November 24

Speaker: Sheng Rao 饶胜 (Wuhan University)

Pretalk: A rough introduction to deformation theory

Abstract: I will introduce several important notions and theorems in the topics within my research in a rough way.

Research talk: Several Rigidity Theorems under Smooth Deformations

Abstract: We report on several rigidity theorems concerning smooth deformations of compact complex manifolds. Two main theorems therein can be described as follows. Let Δ be the unit disk in the complex plane, and consider a smooth family of compact complex manifolds over Δ. We show that the subset of Δ over which the fibers are isomorphic to a fixed hyperbolic manifold is either a discrete subset or all of Δ. Furthermore, for a smooth Kähler family over Δ, we prove a similar rigidity result: the set of points where the fibers are isomorphic to a fixed projective manifold with semiample canonical line bundle is also either a discrete subset or the whole Δ. This talk is based on three preprints jointly authored with Jian Chen, Mu-Lin Li, I-Hsun Tsai, Kai Wang, and Mengjiao Wang.