Math 823: Topics in Complex Analysis

We will cover the $L^2$  theory for the $\overline\partial$ operator and some applications. We will focus on the following topics: Plurisubharmonic functions and pseudoconvex domains. Basic $L^2$ estimates. the Ohsawa-Takegoshi extension theorem and the Skoda division theorem. Siu's theorem on Lelong numbers of plurisubharmonic functions. If time permits, we will discuss the Bergman kernel and its application to the study of biholomorphisms.