Video Lectures

The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This...

In characteristic zero, Castelnuovo proved that every unirational surface is rational. In positive characteristic, this fails dramatically: there exist many non-rational, often even general-type, surfaces that are nevertheless unirational. In 1977...

I will describe recent work in progress on logarithmic--exponential preparation theorems in analytically generated sharply o-minimal structures. Our results imply the sharp o-minimality of ℝexp

as well as a uniform version of Wilkie’s conjecture on...

Discs of stars around super-massive black holes, like the one at the Galactic centre, evolve primarily via resonant relaxation, which is the process governing the evolution of the angular-momentum vectors of stellar orbits about the super-massive...

I'll focus specifically on point counting results in o-minimal structures. I'll start with the classical theorem of Pila and Wilkie and move on to improved versions that only hold in the "sharp" variant of o-minimality.

Let Γ be a countable group with a Cayley graph G. Suppose we are running an independent identical probabilistic algorithm on each vertex (or each edge) and vertices are only allowed to communicate with their neighbors. The goal of this distributed...