Several Complex Variables Seminar

Date: September 4, 2015

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Masanori Adachi , Tokyo University of science

Title: The Diederich-Fornaess index and vanishing theorems

Abstract: The Diederich-Fornaess index is a numerical index that measures hyper convexity of weakly pseudoconvex domains in complex manifolds; in other words, it describes to what extent a domain carries exhaustions by strictly pseudoconvex domains. In this talk, we shall focus on the case of Levi-flat bounded domains and discuss L^2 vanishing theorems which are closely related with the index. We will explain some (non-)vanishing theorems on L^2 holomorphic sections over Levi-flat bounded domains and L^2 CR sections over Levi-flat CR manifolds with emphasis on the role of the index, or a special one-form describing the holonomy of the Levi foliation. The talk is partly based on joint work with Judith Brinkschulte.