Servizio Comunitario di Informazione in materia di Ricerca e Sviluppo - CORDIS

Final Activity Report Summary - GROUPS (European Training Courses and Conferences in Group Theory (Geometric, Analytic and Ergodic Aspects of Group Theory))

This project consisted of a linked series of 7 conferences and training courses in a particular specialised area of pure mathematics, at the interface of geometry, group theory and dynamics. The aim was to bring together experts in these different areas in order for them to cooperated and learn about each other's special skills and benefit from these interchanges, while at the same time exposing doctoral students and young researchers to these new ideas involving the different areas. The conferences took place in Switzerland, Austria, France, Greece and Israel, and many international experts participated, from USA, Russia, Australia, Japan, and many other countries as well as participant European nations.

The conferences and training courses followed the usual structure of mathematics conferences: mini courses of several one-hour talks, and individual one-hour talks on the frontier of current research. The exposure of young researchers and doctoral students to ideas both in their speciality and in nearby fields is an extremely useful part of their training, and such linked conference series are very useful to achieve this. It is hard to describe to the lay person the nature of the specialist fields studied here: the main relationship is between algebraic and geometric structures, in the area of group theory.

In recent years much research has centred around this interface, and this series has brought together experts in the areas of graph theory and expanders (especially events 1 and 5), Mostow rigidity, logic, automorphism groups, outer space and geometric group theory (especially events 2 , 4 and 7), different concepts of boundaries for groups and spaces and actions thereon (events 1 and 6), K-theory and spectral geometry (event 7).

The structure of each event was a residential session with several series of themed, linked mini courses by world experts, aimed at young researchers and experts in related fields: these took the traditional form of one-hour blackboard/power point talks. The main aim of the project was to bring together world experts and young researchers in these different fields, in order to encourage the exchanges that have begun between these areas. We believe that this series of events has done just this.

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75006 PARIS