MAT 543
Complex Analysis II
Several Complex Variables
Tu Th 2:20-3:40 p.m., Psychology A144
First Meeting: 3 September 2002
Instructor
Araceli M. Bonifant
Office: Math Tower 4-107
Phone: 632-8275
Email: bonifant@math.sunysb.edu
About the subject: Several Complex Variables has been an active
subject for decades. The classical work of Poincaré,
F. Hartogs, E. Levi, H. Cartan, K. Oka
and others laid down an important part of the frame work of
the subject. Since then, more and more attention has been
paid to this field, as people discover its deep relationship
with many fundamental problems in classical analysis and geometry,
and its importance for partial differential equations,
complex dynamics, algebraic and symplectic geometry, topology,
quantum field theory and mathematical physics.
Prerequisites: We assume familiarity with the elements of real variable theory, measure theory, one complex variable and functional analysis.
About the course:
- We will recall briefly the elementary theory of functions of a single variable that will be needed for understanding the generalization of certain concepts to higher dimensions.
- Study the elementary properties
of functions of several complex variables (domains of holomorphy, Hartogs theorem, Reinhardt domains, existence theorems for the Cauchy Riemann equations in Runge domains, pseudoconvexity and plurisubharmonicity).
- L2 Estimates and existence theorems for the ${\bar{\delta}}$ operator.
- Stein Manifolds
The topics above are tentative depending on the time available and the
interest of the students.
Textbooks:
- An Introduction to Complex Analysis in Several Variables
by Lars Hörmander
- Function Theory of Several Complex Variables
by Steven G. Krantz