Past Events

Why are certain number theorists seemingly obsessed with Shimuravarieties? Starting from modular curves, I'll give a gentleintroduction to the theory of Shimura varieties. Then I'll discuss therole Shimura varieties play in the Langlands program.

Isoperimetric boundaries minimise area for fixed an enclosed volume, with sharp regularity theory ensuring smoothness away from a closed singular set of codimension seven. I will discuss recent work, with G. Niu, which constructs isoperimetric regions from hypersurfaces in closed manifolds. As a…

Katz-Oda + [BO, section 7]. 

In this talk, I will attempt to survey the recent applications of neural networks to PDEs with a focus on two approaches. I will start by introducing physics-informed neural networks and how they have been applied to discovering unstable singular solutions to fluid equations. Then, I will finish…

The Bateman-Horn conjecture predicts the density of primevalues assumed by integer polynomials. In this talk, we discuss recentprogress on an average version of this conjecture, achieved by employingHooley neutralizers in combination with standard sieving techniques. Inparticular, our findings…

The Anderson tight-binding model describes the transport of quantum particles in disordered environments.  A central question in this model is to understand whether, in the long-time limit, particles diffuse out to infinity or else remain trapped in some bounded region.  In this talk,…

Telescopic stable homotopy theory is an approach to studying the stable homotopy category by decomposing it into atomic periodic pieces, the T(n)-local categories. It is a variant of the approach of chromatic homotopy theory that has…

In this talk, I will discuss the growth rate of Reeb orbits with respect to their period on certain contact manifolds. We focus on fiberwise star-shaped hypersurfaces in the cotangent bundle of a closed manifold. I will explain how a topological condition on the base manifold implies that the…

In 2017, Miller computed the character tables of S_n for all n up to 38 and looked at various statistical properties of the entries. Characters of symmetric groups take only integer values, and based on his computations, Miller conjectured that almost all entries of the character table of S_n…

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, however, are so large that he has described…