School of Mathematics

The conformal bootstrap has proven very powerful for analyzing reflection-positive conformal models. In my talk, I will review this method and suggest a way to generalize it beyond the reflection-positive case, drawing inspiration from the spectral...

A well-known result of Abouzaid says that the wrapped Fukaya category of a cotangent bundle is generated by one cotangent fiber. In the filtered case this is not true, but the filtered Fukaya category comes with a notion of interleaving distance. We...

The Schottky problem is a classical question asking for a characterization of Jacobians among abelian varieties.

In positive characteristic, one may asking whether there are values of discreet invariants known to occurs for abelian varieties which do...

A similarity is a map from Rd to itself that uniformly scales distances. When one repeatedly applies randomly chosen contracting similarities, the resulting Markov chain converges to a limiting stationary distribution known as a self-similar measure...

The quantum connection is a flat connection arising from genus 0 Gromov--Witten theory. They can be defined integrally for sufficiently positive symplectic manifolds, allowing one to consider their characteristic p or p-adic versions which bear...

A central goal in complexity theory is to prove separations between randomized and deterministic models of computation. In communication complexity, a key challenge is to establish lower bounds for multiparty protocols in the number-on-forehead (NOF...

The singularities of integral models of Shimura varieties are encoded in their local models, schemes over the $p$-adic integers whose special fibers are unions of affine Schubert cells. A fundamental question is whether these local models are Cohen...

Homological stability has emerged over the past decades as an organizing principle in topology and beyond. Broadly speaking, many sequences of moduli spaces exhibit the striking phenomenon that their homology stabilizes as the underlying complexity...

The topological entropy of geodesic flows has been extensively studied since the foundational works of Dinaburg and Manning. It measures the exponential complexity of the geodesic flow of a Riemannian manifold, and there are several results...

I will discuss how the Lang–Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber–Pink conjecture for curves in 3. Unlike previous results for curves in g, our result does not rely on any assumption on intersections with...