Van Vu and I have just uploaded to the arXiv our paper “Random covariance matrices: Universality of local statistics of eigenvalues“, to be submitted shortly. This paper draws heavily on the technology of our previous paper, in which we established a...

Assaf Naor and I have just uploaded to the arXiv our paper “Random Martingales and localization of maximal inequalities“, to be submitted shortly. This paper investigates the best constant in generalisations of the classical Hardy-Littlewood maximal...

This is an adaptation of a talk I gave recently for a program at IPAM. In this talk, I gave a (very informal and non-rigorous) overview of Hrushovski’s use of model-theoretic techniques to establish new Freiman-type theorems in non-commutative groups,...

This is the last reading seminar of this quarter for the Hrushovski paper. Anush Tserunyan continued working through her notes on stable theories. We introduced the key notion of non-forking extensions (in the context of stable theories, at least) of...

Starting in the winter quarter (Monday Jan 4, to  be precise), I will be giving a graduate course on random matrices, with lecture notes to be posted on this blog.  The topics I have in mind are somewhat fluid, but my initial plan is to cover a large...