Past Events

The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative...

I will present our recent results on estimating the Lyapunov exponents of weakly-damped, weakly-dissipated stochastic differential equations. Our primary tool is a new, mildly-quantitative version of Furstenberg’s criterion.

A graph drawn in a surface is a k-near-quadrangulation if the product of the lengths of its faces, except for 4-faces, is at most k. Near-quadrangulations play a fundamental role in the theory of 3-colorability of triangle-free graphs on surfaces. We...

Host diversification methods such as within-field mixtures (or field mosaics, depending on the spatial scale considered) are promising methods for agroecological plant disease control. We explore disease spread in host mixtures (or field mosaics)...

There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot...

Calderón's problem (also called electrical impedance tomography) asks the question of whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. I will give a survey of some of the...

Co-evolving network models, wherein dynamics such as random walks on the network influence the evolution of the network structure, which in turn influences the dynamics, are of interest in a range of domains. While much of the literature in this area...

A large body of theory predicts that populations dispersing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its...

Given a smooth plane curve C defined over an arbitrary field k, we say that C is transverse-free if it has no transverse lines defined over k. If k is an infinite field, then Bertini’s theorem guarantees the existence of a transverse line defined...

The structure of the eigenvalues of a quantum system, that is of its spectrum, is crucial to its study. The spectrum of the "ice model" (six vertex model) was computed in the seminal work of Baxter. It has a remarkable form involving polynomials and...