Maths 212: Several Complex Variables, Spring 2016

TuTh 9:30am-11:00am, 891 Evans




Professor  Maciej Zworski
email: zworski@math.berkeley.edu
Office: 801 Evans Hall
Office hours: Tuesday 11-12, Thursday 11-12

Prerequisites:
202AB or equivalent.

Textbooks:
  1. Lars Hörmander, An Introduction to Complex Analysis in Several Variables, 3rd edition, (Chapters I and II)
  2. Lars Hörmander, The Analysis of Linear Partial Differential Operators II (Section 15.1)
  3. Dmitry Khavinson, Holomorphic Partial Differential Equations and Classical Potential Theory (Chapters 1-8)
  4. Johannes Sjöstrand, Analytic microlocal analysis using holomorphic functions with exponential weights

    Syllabus:

    1. Review of the theory of functions of one complex variables
    2. Holomorphy, power series in several complex variables, Hartogs property
    3. Domains of holomorphy, plurisubharmonic functions, pseudoconvex domains
    4. Solving non-homogeneous Cauchy--Riemann equations in spaces defined using global strictly plurisubharmonic weights (Hörmander's L2 estimates)
    5. Solving partial differential equations with holomorphic coefficients: theorems of Cauchy--Kovalevskaya, Zerner and Bony--Shapira
    6. Pseudodifferential operators in complex domains (no background in standard theory is expected or needed)
    7. Fourier integral operators, Egorov's theorem and applications

    Grading:

    You are asked to write a short paper on a research topic related to the course subject, for instance, based on a topic from the texts not covered in class.