Time: 14:00-15:00, Thursday, July 10 2025
Venue：E4-233
Host： Yuan Yuan, ITS
Speaker：Xianghong Gong, University of Wisconsin-Madison
Biography：Professor Xianghong Gong graduated from the University of Chicago in 1994 and is now a professor at the University of Wisconsin-Madison. Before joining Wisconsin in 2000, he held positions at Institute for Advanced Study, University of Michigan, and Oklahoma State University.
Professor Gong is a leading expert in the field of several complex variables and dynamical systems, especially on local holomorphic invariant, regularity of Cauchy-Riemann equation and etc. He published over 40 papers in top journals such as Inventiones Mathematicae, Duke Mathematical Journal, Journal of Differential Geometry.
Title：Integral representations for Cauchy-Riemann solution operators and a global Newlander-Nirenberg problem
Abstract: The study of regularity of the Cauchy-Riemann (d-bar) equation in several complex variables has a long history. In this colloquium, we will present several recent results on the d-bar problem. A common scheme for these solutions is to reproduce differential forms via integral representations. We will explain how the Stein and Rychkov extension operators for function spaces can be used to construct integral formulas. As an application, we will show that the integral representations can be used to study the stability of small deformation of complex structures on domains in a complex manifold.
