This course is an introduction to the theory of functions of
several complex variables, emphasizing the part of the
theory that intersects with analysis and with partial differential
equations.
Here are some of the topics to be discussed.

multivariable power series

Reinhardt domains

domains of convergence

the Hartogs phenomenon

entire functions

integral representations

the Cauchy integral

the Bochner–Martinelli integral

the Bergman kernel function

notions of convexity

linear convexity

polynomial convexity

holomorphic convexity

pseudoconvexity

the Levi problem

the ∂ problem

holomorphic mappings

Course objectives

By the end of the course, you should be able to

describe the similarities and the differences between
one-dimensional function theory and multidimensional function
theory;

explain the concept of domain of holomorphy;

read the research literature on multidimensional
function theory.

Prerequisites

You should have some acquaintance at the first-year graduate
level with both real analysis and single-variable complex analysis.
The official prerequisites for this course are Math 608 and
Math 618 (or equivalents).

During the Fall 2019 semester, my office hour in Blocker 601L is 1:00–2:00 in the afternoon on Tuesday and Thursday; I am available also by appointment. The best way to contact me is via email to boas@tamu.edu. Telephone messages can be left at the main office of the Department of Mathematics, 979-845-7554.