Math 212
: Several Complex Variables, Fall 2021
TuTh 12:30pm-2:00pm, 2 Evans
Professor
Maciej Zworski
email:
zworski@math.berkeley.edu
Office:
801 Evans Hall
Office hours:
Thursday 2:10-3PM or by appointment
Course website:
biweekly homework assignments posted, occasional ZOOM lectures recorded
Prerequisites:
185, 202AB or equivalent.
Textbooks:
Volker Scheidemann,
Introduction to Complex Analysis in Several Variables,
(Chapters 1,2,3,5)
Lars Hörmander,
The Analysis of Linear Partial Differential Operators II
(Section 15.1)
Dmitry Khavinson,
Holomorphic Partial Differential Equations and Classical Potential Theory
(Chapters 1-8)
Lars Hörmander,
The Analysis of Linear Partial Differential Operators I
(Section 9.4)
Johannes Sjöstrand,
Analytic microlocal analysis using holomorphic functions with exponential weights
Syllabus:
The course will concentrate on PDE aspects of the theory and will be largely independendent from 212 given in the Fall of 2019.
Holomorphic functions, Cauchy formula, power series
Biholomorphic maps
The inhomogenous Cauchyâ€“Riemann Differential Equations, Hartogs phenomenon
Solving non-homogeneous Cauchy--Riemann equations in spaces defined using global strictly plurisubharmonic weights (Hörmander's L2 estimates)
Solving partial differential equations with holomorphic coefficients: theorems of Cauchy--Kovalevskaya, Zerner and Bony--Shapira
Pseudodifferential operators in complex domains (no background in standard theory is expected or needed)
Fourier integral operators, Egorov's theorem and applications
Grading:
Based on biweekly homework assignments.