Past lectures

Abstract

The aim of the course is to explore several questions in Asymptotic Geometric Analysis that share a rather surprising feature: their formulation has nothing to do with Probability Theory but their solution is heavily based on probabilistic arguments.

I will use those problems to illustrate two important ideas: that randomness can be used to expose "hidden structures"; and that structure often appears in "extremal situations" (both these rather vague statements will be made clear during the course). Along the way, I will develop the necessary machinery which is important in its own right: it is of constant use in many areas of modern mathematics, statistics and computer science.

Although I will try to make the course as self-​contained as possible, it will require mathematical maturity. Knowledge of some Functional Analysis, measure and integration and probability theory is highly recommended.