Seminar on Complex Analysis and Complex Geometry - Spring 2021

Wednesday, March 3, 2021, 10-11am (Houston time), Zoom (contact Gordon Heier for Zoom meeting access information)

Title: Global non-deformability, super rigidity, and regularity of the complex Neumann problem

Speaker: Yum-Tong Siu, Harvard University

Abstract: Flat directions are the main obstacles for a number of fundamental problems in several complex variables. Among them are the following three.

(i) The global non-deformability of irreducible compact Hermitian symmetric manifolds.

(ii) The strong rigidity and super rigidity problem of holomorphic maps with curvature condition on the target manifold.

(iii) The regularity question of the complex Neumann problem for weakly pseudoconvex domains.

The talk starts with the historic motivations of the problems and does not assume any background more than basic complex analysis. After discussing the general techniques to deal with flat directions and pointing out the similarities and differences in these problems, we will focus on the global non-deformability problem and, in particular, on the case of the complex Grassmannian.