Tuan Tran, Anti-concentration phenomena

Let $X$ be a real random variable; a typical anti-concentration inequality asserts that (under certain assumptions) if an interval $I$ has small length, then $\mathbb{P}(X\in I)$ is small, regardless the location of $I$. Inequalities of this type have found powerful applications in many branches of mathematics. In this talk we will discuss several recent applications of anti-concentration inequalities in extremal combinatorics, as well as random matrix theory. The talk is partially based on joint work with Matthew Kwan and Benny Sudakov.