University of Washington

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...

The talks will be in Paccar Hall Room 291. Abstracts to the talks can be found on the Program page. July 17 : 8:30 - 9: 0 0: Coffee + Opening Remarks 9:00 - 9:30 : Jonathan Novak (UCSD) - Invariant ensembles for coin flippers 9:30 - 10:00: Arnab Sen...

Random walks or diffusions with Dirichlet boundary condition (killing at the boundary) admit a Perron-Frobenius eigenfunction (the unique positive normalized eigenfunction when the domain is bounded). Starting with gambler's ruin problems, we discuss...

There are many synergies between probability theory and convex geometry, especially in high-dimensional settings. We discuss some classical examples and then focus on a recent development concerning a famous theorem of von Neumann, which establishes...

Real-world systems—from academic collaborations and computer networks to biological systems and power grids—are often large, heterogeneous, and highly interconnected. A first step towards understanding these systems is choosing an appropriate...

In this talk I'll give an overview of the mathematical side of the last eight years of my career as a software engineer at Google. This splits into two parts: writing software to automate the planning and management of Google's data centers as part...