**MATH 285K: Spring 2017**

**Spectra of random Schrödinger operators**

lecturer: Marek Biskup, MS 6180

lecture: MWF 10-11 in MS 6201, extra class time/discussion: M 2-4 in MS 6118 (occasionally WF as well)

office hours: (tentatively) MWF 1-2 or just walk in

**Homework: **

**General plan: ** Here is the course announcement.

The aim of the course is to give a thorough introduction to the mathematical theory of Anderson localization including the necessary background from functional analysis, quantum mechanics and material physics. (In particular, no prior exposure to physics will be assumed or required.) Anderson localization is a phenomenon responsible for materials (particularly, superconductors) losing or gaining conductivity depending on the amount of doping by other materials. In a suitable approximation, this can be related to a change of the spectral type of a one-particle Schrödinger operator under random perturbation (a.k.a. disorder). The plan is to discuss known results while highlighting open problems and directions of future research.

**Resources:** We will follow the recent textbook

- Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Graduate Studies in Mathematics, AMS, 2015) by M. Aizenman and S. Warzel

**Organization: **Due to travel plans of the lecturer, the course will be taught in 6 weeks organized in blocks of accelerated activity alternated by idle periods spent, ideally, on the completion of homework assignments. This will require finding two hours of extra time when all participants can meet for additional lectures. This will all be hopefully agreed during the first couple of (regular) lectures.

**Prerequisites:** The prerequisites include a good command of analysis including some exposure to probability and basic functional analysis. All needed concepts and results will still be introduced to give everybody, including the lecturer, proper time to digest them.

**Conditions for getting credit: ** To receive a respectable grade, the participants must successfully complete a majority of homework assignments.