Maths 279: Random perturbations of non-self-adjoint operators, Spring 2021

TuTh 2 PM -- 3:30 PM ZOOM

Professor  Maciej Zworski
Office: 801 Evans Hall
Office hours: by appointment

Basic analysis background, some basic probability theory

  1. Johannes Sjöstrand, Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations, (available via UC Berkeley proxy)
  2. Maciej Zworski Semiclassical Analysis, (for some supplementary and background material -- relevant hand-outs will be available)


    1. Spectral theory of non-self-adjoint operators; examples of spectral instability for linear and non-linear equations
    2. Random perturbations of first order semiclassical differential operators on the circle
    3. Detailed study of perturbations of Jordan block matrices
    4. Introduction to semiclassical analysis; quantum ergodicity for random perturbations
    5. Random perturbations of more general semiclassical operators