Syllabus
PEOPLE AND PLACES:
TOPICS: This course will be an introduction to the spectral theory of random Schroedinger operators and the related properties of solutions to the linear Schroedinger equation. We will discuss Anderson localization and how it can be proved. We will also look at the quantum diffusion conjecture, why it is believed to be true and what partial progress has been made toward understanding it. If there is time we will also discuss some aspects of random matrix theory and the conjectural relationship be relation between the theory of random Schroedinger operators.
PREREQUISITES: In practice much of what we will do can be understood using only undergraduate analysis and linear algebra. However, measure theory and functional analysis do come in at some decisive points.
COURSE WEBSITE: https://sites.google.com/a/msu.edu/jeffrey-schenker/teaching/992-ss17/
HOMEWORK: The book has many exercises. Some exercises from the book will be suggested. These are optional, but it is highly recommend that you work on them. We can take time in class to discuss solutions as appropriate.
PRESENTATIONS: Each participating student should give a lecture at some point in the semester. Potential topics will be mentioned as we go along, but you are encouraged to suggest a topic related to your own research if that is possible.