Maths
279: Random perturbations of non-self-adjoint operators, Spring 2021
TuTh 2 PM -- 3:30 PM
ZOOM
Prerequisites:
Basic analysis background, some basic probability theory
Textbooks:
- Johannes Sjöstrand,
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations,
(available via UC Berkeley proxy)
- Maciej Zworski
Semiclassical Analysis,
(for some supplementary and background material -- relevant hand-outs will be available)
Syllabus:
- Spectral theory of non-self-adjoint operators; examples of spectral
instability for linear and non-linear equations
- Random perturbations of first order semiclassical differential operators on the circle
- Detailed study of perturbations of Jordan block matrices
- Introduction to semiclassical analysis; quantum ergodicity for random perturbations
- Random perturbations of more general semiclassical operators