Past

A scale-invariant moving finite element method is proposed for the

adaptive solution of nonlinear partial differential equations. The mesh

movement is based on a finite element discretisation of a scale-invariant

conservation principle incorporating a monitor function, while the time

discretisation of the resulting system of ordinary differential equations

may be carried out using a scale-invariant time-stepping. The accuracy and

reliability of the algorithm is tested against exact self-similar

solutions, where available, and a state-of-the-art $h$-refinement scheme

for a range of second and fourth order problems with moving boundaries.

The monitor functions used are the dependent variable and a monitor

related to the surface area of the solution manifold.

In Somerville

We review the analytic transformations allowing to construct standard bridges from a semistable Markov process, with indec 1/2, enjoying the time inversion property. These are generalized and some of there properties are studied. The new family maps the space of continuous real-valued functions into a family which is the topic of our focus. We establish a simple and explicit formula relating the distributions of the first hitting times of each of these by the considered semi-stable process

When two single server queues have the same arrivals process, this is said to be a `fork-join queue'. In the case where the arrivals and service processes are Brownian motions, the queue lengths process is a reflecting Brownian motion in the nonnegative orthant. Tan and Knessl [1996] have given a simple explicit formula for the stationary distribution for this queueing system in a symmetric case, which they obtain as a heavy traffic limit of the classical discrete model. With this as a starting point, we analyse the Brownian model directly in further detail, and consider some related exit problems.

The Farrell-Jones Conjecture predicts that the algebraic K-Theory of a group ring RG can be expressed in terms of the algebraic K-Theory of the coefficient ring R and homological information about the group. After an introduction to this circle of ideas the talk will report on recent joint work with A. Bartels which builds up on earlier joint work with A. Bartels, T. Farrell and L. Jones. We prove that the Farrell-Jones Conjecture holds in the case where the group is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The result holds for all of K-Theory, in particular for higher K-Theory, and for arbitrary coefficient rings R.

Let M be an ordered vector space over an ordered division ring, and G a definably compact, definably connected group definable in M. We show that G is definably isomorphic to a definable quotient U/L, where U is a convex subgroup of M^n and L is a Z-lattice of rank n. This is a joint work with Panelis Eleftheriou.

We derive a two-dimensional compressible elasticity model for thin elastic sheets as a Gamma-limit of a fully three-dimensional incompressible theory. The energy density of the reduced problem is obtained in two

steps: first one optimizes locally over out-of-plane deformations, then one passes to the quasiconvex envelope of the resulting energy density. This work extends the results by LeDret and Raoult on smooth and finite-valued energies to the case incompressible materials. The main difficulty in this extension is the construction of a recovery sequence which satisfies the nonlinear constraint of incompressibility pointwise everywhere.

This is joint work with Sergio Conti.