Past Events

In this talk, we consider analogs of Jaeger's circular flow conjecture and its dual Jaeger-Zhang conjecture in signed graphs. We will first give the notions of circular coloring and circular flow in signed graphs, and then show that every (6k-2)-edge...

The first two problems are concerning edge-colorings of complete graphs. Erd\H{o}s and Tuza asked in 1993 whether for any graph F on l edges and any completely balanced coloring of any sufficiently large complete graph using l colors contains a...

I will begin by introducing the Penrose tiling -- the most famous example of a self-similar quasi-periodic pattern. In addition to its beauty and mathematical interest, this pattern has a famous physical application to exotic materials called...

The Szemeredi-Trotter Incidence Theorem, a central result in geometric combinatorics, bounds the number of incidences between n points and m lines in the Euclidean plane. Replacing lines with circles leads to the unit distance problem, which asks how...

Detecting differences and building classifiers between distributions, given only finite samples, are important tasks in a number of scientific fields. Optimal transport (OT) has evolved as the most natural concept to measure the distance between...

Lyapunov exponents and Oseledets spaces are a rough analogue of eigenvalues and eigenspaces for stationary products of matrices (or operators). We are interested in the stability or otherwise of these exponents and spaces when the family of matrices...

The endothelial lining of blood vessels presents a large surface area for exchanging materials between blood and tissues. The endothelial surface layer (ESL) plays a critical role in regulating vascular permeability, hindering leukocyte adhesion as...

This talk addresses the moduli space of complete, conformally flat metrics metrics on a sphere with k punctures having constant positive Q-curvature and positive scalar curvature. Previous work has shown that such metrics admit an asymptotic...

In this talk, I discuss a pure-exchange economy with no aggregate uncertainty, and I characterize in closed-form and in full generality Pareto-optimal risk-sharing allocations between two agents who maximize rank-dependent utilities (RDU). I then...

Given a smooth function Φ:ℝ→ℝd, we ask whether every Borel subset of ℝd with sufficiently high Hausdorff dimension contains a pair of the form {x,x+Φ(t)} with Φ(t)≠0. We prove that a large class of ``curved” functions have this property while certain...