Past Events

Abstract: A new frontier for the modeling and analysis of reaction-diffusion PDE systems is where the diffusing species are nonlinearly coupled through dynamic interactions on the domain boundaries. Some specific examples of such systems, including...

The Rudin-Shapiro polynomials $p_{m}$ were first studied by Rudin, Shapiro, and Golay independently nearly 80 years ago and are defined recursively by $p_{0}(x) = q_{0}(x) = 1$ and $$ p_{m}(x) = p_{m-1}(x) + x^{2^{m-1}} q_{m-1}(x), $$ $$ q_{m}(x) = p...

In this talk we will discuss recent results concerning stochastic (and deterministic) free boundary problems, particularly arising in fluid structure interaction (FSI). We will begin by considering a nonlinearly coupled FSI system perturbed by...

Networks are everywhere in biology - from molecules that interact within a cell to neurons that communicate across the brain. Understanding how signals flow through these networks is key to uncovering how biological systems function - and how they...

Pick your favorite manifold M and a positive integer r : how many r rank (topological) complex vector bundles are there over M up to isomorphism? While the question is accessible via K-theory in the stable range, unstably such bundles become much...

The Haglund--Haiman--Loehr theorem (2005) provides a combinatorial formula for the modified Macdonald polynomials, highlighting the surprising connections between modified Macdonald polynomials and combinatorial statistics such as the major index and...

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local...

In this talk, I will describe the mathematics behind proving lower bounds on quantum circuit depth using light-cone arguments. These arguments have been used to prove lower bounds on the complexities of physically relevant ground states. No quantum...

A classical problem in signal recovery is to determine whether a finite signal can be recovered from its Fourier transform with missing values. This problem has been studied by many authors starting with the seminal papers by Matolsci and Szuks in...

Given a finite transitive group G ≤ Sym(Ω), a set F ⊂ G is intersecting if for any g, h ∈ G, there exists ω ∈ Ω such that ω g = ω h . The intersection den- sity ρ(G) is the maximum ratio of |F| |Gω| , where F runs through all intersecting sets of G...