**R. Sivaguru**

TIFR

October 8, 2015

**Several Complex Variables: a Sampler**:
The aim of this talk is to describe a selection of problems and lines of enquiry that are of significant interest in several complex variables. In broad terms, these questions explore the relationship between function theory and boundary geometry on smoothly bounded domains in $mathbb{C}^n$, $n>1$. We will begin by introducing and motivating the basic objects of study before proceeding to describe these problems and known results. We will focus on the $ar{partial}$-Neumann problem, Bergman projection/kernel, extension of biholomorphic maps, and related ideas.