Past Events

The zero Debye length asymptotic of the Schrodinger-Poisson system in Coulomb gauge for ill-prepared initial dada is studied. We prove that the Debye length to the current density defined by the solution of the Schrodinger-Poisson system in Coulomb...

Let f be the obvious covering map from Euclidean n-space to the n-torus. It is well known that if L is any straight line in n-space, then the closure of f(L) is a very nice submanifold of the n-torus. In 1990, Marina Ratner proved a beautiful...

We will discuss continuous-time, multi-type branching problems to model aspects of HIV-virus and T-cell dynamics in the blood stream. We are motivated by observations of viral load in HIV+ patients on anti-retroviral treatment (ART). While on ART for...

A gene family is a set of genes, present in the genomes of several genomes, possibly in multiple occurrences in some genomes, that all originates from a single ancestral gene. A gene tree is a binary tree that describes evolutionary relationships...

In the context of optimal control, the Hamilton-Jacobi Partial Differential Equation (HJ PDE) is a continuous analogue to the discrete Bellman dynamic-programming equation. Both of these equations satisfy a causal property: the solution value at a...

I will discuss recent results concerning the regularity of the extremal solution associated with fourth order nonlinear eigenvalue problems on general domains. We show that the extremal solution is bounded under various assumptions on the...

In 2009, Büyükboduk published a result in Crelle which expressed the order of the $\chi$-part of the class-group of a number field ($\chi$ a $p$-adic character of a Galois group) in terms of $L$-functions and regulators. The proof used Kolyvagin...

Coisotropic submanifolds of symplectic manifolds are canonically foliated. Their deformation is described by an L-infinity algebra with a known geometric description. I will describe some calculations with the obstruction theory of this L-infinity...

(0,1)-matrices are, in particular, nonnegative matrices, and so the Perron-Frobenius theory of nonnegative matrices applies to them. Thus they have a nonnegative eigenvalue that is at least as large as the magnitude of all other eigenvalues...

I will talk about work with Dan Isaksen on the motivic homotopy groups of spheres, focusing on the story of the Hopf maps. In classical algebraic topology the Hopf maps generate a very small and easily computed subring of the stable homotopy ring...