University of Washington

Not all convex functions have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral space, a compact extension of...

I will review the progress of large language models for mathematics over the last 3 years, from barely solving high school level mathematics to solving some minor open problems in convex optimization, combinatorics and probability theory. The...

A good way to understand the structure of a finite group is through its representations. The family of representations of a group on a fixed field has several properties: it is closed by finite direct sums, by tensor products, it contains the dual...

An abstract discrete dynamical system consists of a set X and a self-map f from X to itself. Dynamics studies the orbits of points of X under repeated application of f. When X and f are defined by polynomials, algebraic geometry comes into play, and...

I will review a topic in mathematical physics, called Lieb-Robinson bounds, that exemplifies analysis, geometry, and dynamics. These bounds describe the dynamics of a physical system of many interacting quantum degrees of freedom: they control how...

There is an emerging interest in understanding the behavior of partial differential equations on graphs G=(V,E). The classic approach is to think of a graph as a (discretized) compact manifold without boundary (since there is no `complement', no...

The capillary energy functional models the equilibrium shape of a liquid drop meeting a substrate at a prescribed interior contact angle. We will discuss a rigidity theorem for volume-preserving critical points of the capillary energy in the half...

A central question in quantum chaos is how classical chaotic dynamics influence quantum behavior. On compact Riemannian manifolds, pure quantum states correspond to Laplacian eigenfunctions. The quantum unique ergodicity (QUE) conjecture of Rudnick...

We consider a region in the complex plane enclosed by a deltoid curve inscribed in the unit circle, and define a family of polynomials that satisfy the same recurrence relation as the Faber polynomials for this region. We use this family of...