题 目：Levi's problem, convexity, and squeezing functions on bounded domains
主讲人概况：邓富声，中国科学院大学副教授，博士。主要从事多复变与复几何、数学物理的研究，在《Trans. Amer. Math.Soc.》和《Math. Z. 》等期刊发表论文10余篇。
报告摘要： After giving a brief review of the classical Levi's problem for bounded domains and it's relation to convexity, we introduce a stronger version of it which says that a boundary point of a strongly seudoconvex domain can be globally convexified. This was proved in a deep work of Dederiech-Fornaess-Wold. We discuss a generalization of it to general complex spaces. We then introduce the notion of squeezing function on bounded domains, a concept that motivated the above convexification problem. The key insight in this concept is boundary estimate. We will discuss boundary behavior of squeezing functions on planer domains and genenral strongly pseudoconvex domains. Squeezing functions on projective manifolds will also be discussed briefly.