Workshop Reports 2005 

This page holds short reports on ICMS workshops
from June 2005 onwards.
Each short report is followed by links to the pdf file of a more
detailed report and the workshop's original webpages where you will
find the timetable and list of participants.
Probabilistic Limit Laws for Dynamical Systems 13 17 JuneFor the simplest chaotic (but deterministic) dynamical systems, it is often the case that ``loss of memory'' or decay of correlations occurs exponentially quickly so that timeseries measurements are only weakly dependent and obey the laws encountered in elementary probability such as the strong law of large numbers and the central limit theorem.In recent years, it has been recognised that for the kinds of dynamical systems that typically arise in applications often either the elementary probability techniques fail, or the statistical laws satisfied by the system are not standard (slow decay of correlations, noncentral limit theorem behaviour), or both. An important programme has been to understand such systems. By importing and developing a wide range of techniques from probability theory into the study of dynamical systems, the class of systems for which we have a good understanding of statistical properties has broadened dramatically in the last ten years. Many of these recent insights were the work of conference participants, and the workshop was an opportunity to share their latest results and techniques. The ensuing discussions generated many new and significant ideas for progress in this area of research. Workshop timetable and participants  Detailed Report (pdf file) Algebraic K and Ltheory of Infinite Groups 27 June1 JulyManifolds are a largescale generalization of standard Euclidean space, and the most important topological spaces for applications to geometry and physics. The topology of manifolds is closely related to the algebraic properties of modules and quadratic forms over the fundamental group rings. Current research is particularly concerned with infinite groups, where there is a deep interplay between the geometry and algebra. Many of the striking advances made in this field have come from the application of geometric methods to algebraic problems. Geometric group theory has uncovered fascinating new phenomena in the world of infinite discrete groups. On the other hand, the central conjectures of Borel, Novikov and FarrellJones have only been verified for groups which connect fairly closely to nonpositively curved geometries. The purpose of the meeting was to bring together leading researchers in these fields, both to report on their results and to introduce the subject to a younger generation of mathematicians.Workshop timetable and participants  Detailed Report (pdf file) CoagulationFragmentation Processes: Theory and Application 48 JulyThe workshop dealt with mathematical and modelling aspects of coagulationfragmentation processes. Such processes are of importance in describing phenomena in many areas of natural sciences, for example in controlled manufacturing of nanoparticles, molecular beam epitaxy and at the same time in the formation of planetoids. Mathematically, these processes are described by systems of ordinary differential or integrodifferential equations. They pose deep analytical and numerical questions and constitute an active area of research. In this area there is a wide scope for interaction between analysts working on both deterministic and stochastic models, numerical analysts, modellers and experimentalists. All these specialisations were well represented at the workshop. A variety of presentations were made at the meeting; fifteen invited speakers gave hourlong talks, and a further twelve shorter contributed talks were also given. As well as providing a forum where experts from the same area reported their most recent results, several talks served to introduce delegates to new methods of analysis and areas of application.Workshop timetable and participants  Detailed Report (pdf file) Optimal Transportation, Transport Equations and Hydrodynamics 1117 JulyOptimal Transportation Theory comprises the recent developments related to the classical Monge mass transfer problem, where a mapping is sought that transforms one prescribed finite measureinto another, while minimising a specified cost functional. This subject derived a great impetus from Brenier's work of the late 1980s providing a monotone mapping solving the Monge problem with a quadratic cost, and the subsequent Caffarelli regularity theory. The socalled Brenier map (styled map with convex potential by Caffarelli) has acquired a wide range of applications to geometric inequalities and optimisation problems, and many of the latest developments were discussed at the workshop.Transport equations describe how a scalar field evolves under the flow of a vector field; the Di PernaLions theory of the late 1980s showed how to deal with nonsmooth vector fields having Sobolev regularity by introducing the notion of renormalised solution, and recent work of Ambrosio has accommodated vector fields of bounded variation, using a different method derived from geometric measure theory. The later result had been expected for many years and has a wide range of applications, as well as deep connections with the theory of multidimensional systems of hyperbolic conservation laws, one of the most challenging field in nonlinear PDEs. The vorticity equation of planar hydrodynamics comprises a transport equation whose vector field is the fluid velocity, coupled with the BiotSavart law to calculate the velocity in terms of the vorticity. In recent years Cullen and his collaborators have been developing a mathematical theory for the semigeostrophic model of ocean and atmosphere dynamics, which has a formulation expressing the dynamics in terms of an optimal transportation problem, and a dual formulation involving a transport equation by a vector field of bounded variation, so that it impinges on all three themes of the meeting. Workshop timetable and participants  Detailed Report (pdf file) Workshop
on Dynamical Problems in Mathematical Materials Science
Over the past 20 years, mathematical materials science has become a
vibrant discipline, with a very significant impact both on mathematics 

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