Previous Conferences & Workshops

In this talk, I will present joint work with Charles Bordenave and Mostafa Sabri establishing quantum ergodicity and quantum weak mixing for sequences of finite Schreier graphs converging, in the Benjamini–Schramm sense, to an infinite Cayley graph...

The regularity lemma says that every discrete object can be partitioned into a small number of random-like subobjects. But how small is small? And can we make small smaller if we assume that our given object is simple? And what does it mean for a...

I will discuss some joint work with Bhargav Bhatt and Mark Kisin, in which we use prismatic methods to obtain new structures on Breuil—Kisin modules, and deduce results on the inertial weights of the reduction mod $p$ of local $p$-adic Galois...

Essentially optimal estimates have been obtained for mean values of Vinogradov’s exponential sum as a consequence of the decoupling method (by Bourgain, Demeter and Guth), and the efficient congruencing method (by the speaker). Such work makes...

The very first result ever proved about tournaments is due to Rédei, who nearly 100 years ago proved that every tournament contains a Hamiltonian directed path. Since then, questions and results about directed paths in tournaments have become a...

Consider a collection of forms of odd degree with rational coefficients. Birch proved in 1957 that if the number of variables is sufficiently large, then the forms must have a nontrivial rational zero. The bounds resulting from Birch's proof...

I will discuss questions pertaining to geometric unlikely intersections and transcendence in the setting of torii in positive characteristic. This is based on work in progress joint with Anup Dixit, Philip Engel, and Ruofan Jiang.