I will give an overview of the main results and challenges in the statistical mechanics of disordered systems and spin glasses. Some of these challenges are closely related to understanding the properties of extreme values of high-dimensional random fields. I will discuss this in the examples of the random energy model, the generalised random energy model, and branching Brownian motion. If there will be time, I may also discuss some implication on the dynamics of such systems.

* The second lecture will take place on Tuesday, May 8 (13:30-15:30) at Room 110, RIMS.