School of Mathematics

I will discuss pointwise ergodic theory as it developed out of Bourgain's work in the 80s, leading up to my work with Mirek and Tao on bilinear ergodic averages.

Let C be a class of metric spaces. We consider the following computational metric embedding problem: given a vector x in R^{n choose 2} representing pairwise distances between n points, change the minimum number of entries of x to ensure that the...

A finite set system is union-closed if for every pair of sets in the system their union is also in the system.  Frankl in 1979 conjectured that for any such system there exists an element which is contained in ½ of the sets in that system (the only...

In 1996 Manjul Barghava introduced a notion of P-orderings for arbitrary sets S of a Dedekind domain, with respect to a prime ideal P, which defined associated invariants called P-sequences. He combined these invariants to define generalized...

Given a convex billiard table, one defines the set  swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating function. I...

P-adic non abelian Hodge theory, also known as the p-adic Simpson correspondence, aims at describing p-adic local systems on a smooth rigid analytic variety in terms of Higgs bundles. I will explain in this talk why the « Hodge-Tate stacks »...

Discrepancy theory provides a powerful approach to improve upon the bounds obtained by a basic application of the probabilistic method. In recent years, several algorithmic approaches have been developed for various classical results in the area. In...

A Lagrangian cobordism between Legendrian knots is an important notion in symplectic geometry. Many questions, including basic structural questions about these surfaces are yet unanswered. For instance, while it is known that these cobordisms form a...

Matrix powering, and more generally iterated matrix multiplication, is a fundamental linear algebraic primitive with myriad applications in computer science. Of particular interest is the problem’s space  complexity as it constitutes the main route...

While conducting a series of number-theoretic machine learning experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious oscillation in the averages of Frobenius traces of elliptic curves over Q.  If one computes the average value of a_p(E) for...