The cross-fertilization of ideas from abstract group theory with those from geometry, the use of topological and cohomological techniques have contributed over recent years to revitalising group theory and representation theory in many exciting ways. Not only has this brought impressive mathematical advances, but again it has drawn in different kinds of specialists. At this London Mathematical Society Symposium we aimed to draw together experts in algebra, geometry, representation theory and cohomology to make a contribution to this interchange of ideas. It is an area where there is marked strength in the United Kingdom, traditionally the home of many group theorists, but nowadays also active in cohomological and geometric group theory.
The closing report to the Science and Engineering Research Council began thus:
“The success of this meeting owed much to the strong list of participants, the high standard of lectures by invited speakers and to the good environment at Grey College which encouraged many collaborative research projects. The success can be measured by the strength of the articles which we are assembling for the Conference Proceedings.”
We thank all those authors whose articles were submitted for this volume, and also the equal number of referees. We emphasise that every effort was made to have papers refereed to the same standard as academic and learned mathematical journals. There are a number of survey articles here including those by Carlson, Cornick, Grigorchuk, Linnell, Mikhajlovskii and Ol'shanskii, and Wilson.