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
Here are some of the topics to be discussed.
multivariable power series
domains of convergence
the Hartogs phenomenon
the Cauchy integral
the Bochner–Martinelli integral
the Bergman kernel function
notions of convexity
the Levi problem
the ∂ problem
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
explain the concept of domain of holomorphy;
read the research literature on multidimensional
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 firstname.lastname@example.org. Telephone messages can be left at the main office of the Department of Mathematics, 979-845-7554.