Fall semester, October 2009 - January 2010

**Lecturer **

Bo'az Klartag

Room 229, Schreiber building

Phone: 03-6406957

**Classes**

Tuesday, 16-18, Kaplun 319

Wednesday 16-17, Shenkar 13-14

**Final grade**

There will be 3-5 home assignments throughout the semester.

**Recommended literature** All of the following books are available at the library:

- L. Hormander, An introduction to complex analysis in several variables (we will cover chapters 1,2 and 4).
- B. Shabat, An introduction to complex analysis, part II (translation from Russian).
- S. Krantz, Function theory of several complex variables (more detailed).
- R. Narasimhan, Several Complex Variables.
- M. Herve, Several Complex Variables.

**Syllabus **

Functions in several complex variables, pluriharmonic functions, holomorphic and biholomorphic mappings. The phenomenon of forced analytic continuation, Hartogs extension theorem, Reinhardt domains. Domains of holomorphy, d-bar equation. Subharmonic and plurisubharmonic functions, pseudoconvex sets, analogy with real-variable convexity. Existence theorems for d-bar equation, Levi's problem. Prekopa-Leindler and Berdntsson's inequalities, applications to convex geometry.

**Exercises **

The grades of the exercises.