Past

We study the parabolic Anderson problem, i.e., the heat equation on the d-dimentional

integer lattice with independent identically distributed random potential and

localised initial condition. Our interest is in the long-term behaviour of the

random total mass of the unique non-negative solution, and we prove the complete

localisation of mass for potentials with polynomial tails.

Team meetings, held roughly every four weeks, are open to anyone who is

interested. OxMOS post docs and Dphil students will give updates on the

research.

I'll include a rather short proof of this connectedness in a group of finite

Morley rank, but I'll maybe spend most of the time talking about related matter

without giving proofs.

The numerical study of lattice quantum chromodynamics (QCD) is an attempt to extract predictions about the world around us from the standard model of physics. Worldwide, there are several large collaborations on lattice QCD methods, with terascale computing power dedicated to these problems. Central to the computation in lattice QCD is the inversion of a series of fermion matrices, representing the interaction of quarks on a four-dimensional space-time lattice. In practical computation, this inversion may be approximated based on the solution of a set of linear systems.

In this talk, I will present a basic description of the linear algebra problems in lattice QCD and why we believe that multigrid methods are well-suited to effectively solving them. While multigrid methods are known to be efficient solution techniques for many operators, those arising in lattice QCD offer new challenges, not easily handled by classical multigrid and algebraic multigrid approaches. The role of adaptive multigrid techniques in addressing the fermion matrices will be highlighted, along with preliminary results for several model problems.

First I will introduce Poisson random measures and their connection to Levy processes.  Then SPDE

One natural question in interpolation theory is: given a finite set of points

in R^n, what is the least degree of polynomials on R^n needed to induce every

function from the points to R? It turns out that this "interpolation degree" is

closely related to a fundamental measure of complexity in algebraic geometry

called Castelnuovo-Mumford regularity. I'll explain these ideas a new

application to projections of varieties.