School of Mathematics

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...

The Yang-Mills-Higgs (YMH) model plays a central role in several areas of mathematics, including analysis, geometry, and probability theory. In this talk, we implement the stochastic quantization procedure for the YMH model in two dimensions. That...

I will discuss a recent notion - called categorical approximability - that extends the property of precompactness of a metric space. This is applied to certain spaces of Lagrangian submanifolds endowed with the spectral metric, such as exact...

This talk will recall the Birch--Swinnerton-Dyer Conjecture and describe highlights of the progress towards it, both pre- and post-millennium.  This will largely be a repeat of the speaker's plenary talk from the 2025 Clay Research conference on the...

What is the relative computational power of time and space? Tree evaluation (TreeEval) has become a central problem in understanding this question, especially after its application by Williams (STOC 2025, IAS CSDM seminar 9/23/25) to prove a...

I will discuss some recent work establishing the orderability of contact manifolds which arise as a quotient of an aspherically fillable manifold by a finite group action which extends (non-freely) to the filling. This generalizes the well known...

The local intertwining relation (LIR) is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. It plays a central role in Arthur’s endoscopic classification for...