Previous Conferences & Workshops

Nazarov and Sodin have shown that the zero set of a random real homogeneous polynomial in n+1 variables and of large degree has many components and the same is true for the random harmonic such polynomial ("mono-chromatic waves") .We show that for...

By imposing symmetry on manifolds of exceptional holonomy we get a variety of differential geometric questions in lower dimensions. Related to that, one can consider “adiabatic limits”, where the manifold has a fibration and the fibre size is scaled...

This talk will be an exposition of a circle of ideas that concerns the cohomology of arithmetic groups and the special values of certain automorphic L-functions. I will explain some recent results about the critical values of (1) Rankin-Selberg L...

Three fundamental factors determine the quality of a statistical learning algorithm: expressiveness, optimization and generalization. The classic strategy for handling these factors is relatively well understood. In contrast, the radically different...

We will discuss the constructions of compact manifolds with exceptional holonomy (in fact, holonomy $G_{2}$), due to Joyce and Kovalev. These both use “gluing constructions”. The first involves de-singularising quotient spaces and the second...

I will try to explain what the Fourier expansion of a "modular form" on an exceptional group looks like, from the point of view of the archimedean place. In more detail, Gross-Wallach and Gan-Gross-Savin have singled out what a modular form on an...

In this lecture we will review the notion of the holonomy group of a Riemannian manifold and the Berger classification. We will discuss special algebraic structures in dimensions 6, 7 and 8, emphasising exterior algebra, and then go on to...

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its...

I will present the proof of the split-generation of the compact Fukaya categories of certain Milnor fibers by vanishing cycles. The proof is based on the verification of the Koszul duality between compact and wrapped Fukaya $A_\infty$ algebras of...