: Several Complex Variables, Fall 2021
TuTh 12:30pm-2:00pm, 2 Evans
801 Evans Hall
Thursday 2:10-3PM or by appointment
biweekly homework assignments posted, occasional ZOOM lectures recorded
185, 202AB or equivalent.
Introduction to Complex Analysis in Several Variables,
The Analysis of Linear Partial Differential Operators II
Holomorphic Partial Differential Equations and Classical Potential Theory
The Analysis of Linear Partial Differential Operators I
Analytic microlocal analysis using holomorphic functions with exponential weights
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
The inhomogenous Cauchy–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
Based on biweekly homework assignments.