Math 212: Several Complex Variables, Fall 2021

TuTh 12:30pm-2:00pm, 2 Evans

Professor  Maciej Zworski
Office: 801 Evans Hall
Office hours: Thursday 2:10-3PM or by appointment
Course website: biweekly homework assignments posted, occasional ZOOM lectures recorded

185, 202AB or equivalent.

  1. Volker Scheidemann, Introduction to Complex Analysis in Several Variables, (Chapters 1,2,3,5)
  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. Lars Hörmander, The Analysis of Linear Partial Differential Operators I (Section 9.4)
  5. Johannes Sjöstrand, 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.

    1. Holomorphic functions, Cauchy formula, power series
    2. Biholomorphic maps
    3. The inhomogenous Cauchy–Riemann Differential Equations, Hartogs phenomenon
    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


    Based on biweekly homework assignments.