Past Events

Exponential sums play a role in many different problems in number theory. For instance, Gauss sums are at the heart of some early proofs of the quadratic reciprocity law, while Kloosterman sums are involved in the study of modular and automorphic...

In 1974 Erdős and Rothschild asked the following question: given integers k, s and a large n, what is the maximum number of s-edge-colourings of an n-vertex graph free of a monochromatic k-vertex clique? A follow up question is to determine which...

The central objects in this talk are the descent polynomials of colored permutations on multisets, referred to as colored multiset Eulerian polynomials. These polynomials generalize the colored Eulerian polynomials that appear frequently in algebraic...

Inferring graphs of interactions between genes has become a textbook case for high-dimensional statistics, while models describing gene expression at the molecular level have come into their own with the advent of single-cell data. Linking these two...

Before the winter break we saw a number of key structures of deformation theory: differential graded Lie algebras, the Maurer-Cartan equation and its gauge group, and L-infinity algebras. In this talk, we will see how such structures arise in the...

An algebraic variety is a central object of study in algebraic geometry. A special kind of algebraic variety has caught the attention of analysts recently. These are called distinguished varieties because they intersect the topological boundary of a...

In this talk, we prove that |ζ(σ+it)|≤ 70.7 |t|4.438(1-σ)^{3/2} log2/3|t| for 1/2≤ σ ≤ 1 and |t| ≥ 3, combining new explicit bounds for the Vinogradov integral with exponential sum estimates. As a consequence, we improve the explicit zero-free region...

The study of ordered Ramsey numbers of monotone paths for graphs and hypergraphs has a long history, going back to the celebrated work by Erdos and Szekeres in the early days of Ramsey theory. We obtain several results in this area, establishing two...

We consider an arbitrary sequence of d*d matrices (A_n) of norm at most 1 and subject them to noiselike perturbations of size epsilon. We show that the perturbed system has simple Lyapunov spectrum (no repeated exponents) and discuss universal bounds...

Extremal graph theory studies the question of how dense a graph (or hypergraph) can globally be while still avoiding a given local structure. This global-to-local theme is also a key feature of the field of property testing, which deals with the...