Video Lectures

We prove this bound by first using the unitary Ichino-Ikeda formula of N. Harris to relate the central L-value to an automorphic period integral.  There is a `trivial' bound for this integral, which turns out to correspond to the convexity bound for...

The goal of this talk is to present new results dealing with the asymptotic joint independence properties of commuting strongly mixing transformations along polynomials. These results form natural strongly mixing counterparts to various weakly and...

If f is a real polynomial and A and B are finite sets of cardinality n, then Elekes and Ronyai proved that either f(A×B) is much larger than n, or f has a very specific form (essentially, f(x,y)=x+y). In the talk I will tell about an analogue of...

Given an area-preserving surface diffeomorphism, what can one say about the topological properties of its periodic orbits? In particular, a finite set of periodic orbits gives rise to a braid in the mapping torus, and one can ask which isotopy...

Zeros of L-functions have been extensively studied, due to their close connection to arithmetic problems. Despite several precise conjectures about their behavior, our unconditional understanding of them remains limited. In this talk we will discuss...

Several classical results in Ramsey theory (including famous theorems of Schur, van der Waerden, Rado) deal with finding monochromatic linear patterns in two-colourings of the integers.  Our topic will be quantitative extensions of such results.  A...

At the beginning of the 20th century, Syrian Catholic priest Paul Sbath (Aleppo, 1887 – Aleppo, 20 October 1946) obtained and consolidated a collection of 1,325 manuscripts, mainly acquired between Aleppo, Jerusalem, and Cairo. In 1927, Sbath sold...

Planar last passage percolation models are canonical examples of stochastic growth, polymers and random geometry in the Kardar-Parisi-Zhang universality class, where one considers oriented paths between points in a random environment accruing the...

The question of stability of approximate group homomorphisms was first formulated by Ulam in the 1940s. One of the most famous results in this area is Kazhdan's 1982 result on stability of approximate unitary representations of an amenable group...

The duality long exact sequence relates linearised Legendrian contact homology and cohomology and was originally constructed by Sabloff in the case of Legendrian knots. We show how the duality long exact sequence can be generalised to a relative...