Video Lectures

I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations.

The proof is based on the construction of contact capacities coming from spectral selectors defined on the...

We show that for every quadratic extension of number fields K/F, there exists an abelian variety A/F of positive rank whose rank does not grow upon base change to K. By work of Shlapentokh, this implies that Hilbert's tenth problem over the ring of...

Stars orbiting sufficiently close to massive black holes inevitably inspiral towards the black hole due to gravitational wave radiation. The fate of such stars is subtle and depends on an interplay between tidal heating of the star, mass transfer...

I will start by a gentle introduction to operadic structures by drawing a parallel with classical associative structures. Then we will see how those structures can be applied to matroid theory via three examples: Chow rings, Orlik--Solomon algebras...

We consider the space of configurations of n points in the three-sphere S3, some of which may coincide and some of which may not, up to the free and transitive action of SU(2) on S3. We prove that the cohomology ring with rational coefficients is...

Every braid can be thought of as a homeomorphism of a punctured disc. Morally, the more complicated a braid is, the more dynamics is contained in the corresponding homeomorphism, which one can quantify using topological entropy. In particular, one...

More than 120 years ago, Minkowski published a seminal paper that laid the foundation for the field of convex geometry (as well as several other areas of mathematics). Despite numerous advances in the intervening years, there are fundamental...

We will explore certain C0-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms. We...

Positive selector processes are natural stochastic processes driven by sparse Bernoulli random variables. They play an important role in the study of suprema of general stochastic processes, and in particular, Talagrand posed the selector process...

On-shell methods have found a new application to local observables such as asymptotic radiation fields and gravitational waveforms. While these observables are invariant under small gauge transformations, they are known to depend on a choice of...