Past Events

We establish explicit criteria of solvability for the quasilinear Riccati type equation $-\Delta_p u =|\nabla u|^q + \omega$ in a bounded $\mathcal{C}^1$ domain $\Omega\subset\mathbb{R}^n$, $n\geq 2$. Here $\Delta_p$, $p>1$, is the $p$-Laplacian, $q$...

Continuum traffic theories whereby individual vehicles are collectively modeled have enjoyed a rich history since their popularization by M.J. Lighthill and G.B. Whitham. These models are able to elucidate the dynamics of ``phantom jams,'' transient...

Motivated by geometry, we consider a `less discrete' way of counting lattice points in polytopes, in which one assigns a certain `weight' to each lattice point. On the combinatorial side, this approach reveals some `hidden symmetry' which improves...

We will discuss our motivation for understanding what the analogue of DeRham cohomology should be for E_{\infty}-algebras in connection with algebraic K-theory and topological cyclic homology.

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...