Workshop: Finite presentations of finite and infinite groups

Over the past decade the study of so-called Curtis-Phan-Tits theory has extended from its original motivation which was to provide tools for the revision of the classification of the finite simple groups to results on finite presentability of (unitary forms of) Kac-Moody groups over finite fields and S-arithmetic groups. These developments in Curtis-Phan-Tits theory are in the realm of finiteness properties of lattices in locally compact groups. Independently, the Curtis-Tits theorem, one of the fundamental results that inspired the Curtis-Phan-Tits theory, was used to prove that all non-abelian finite simple groups with the possible exception of the Ree groups have presentations with two generators and at most 80 relations. Further advances both in finiteness properties of lattices in locally compact groups, in Curtis-Phan-Tits theory and in bounded presentations of discrete groups are to be expected by exploiting the methods of these areas of mathematics simultaneously. For this reason we think that it is appropriate and timely to organize a workshop at Birmingham bringing together researchers active in these spheres.

As described in the case for support, we expect an academic impact of the proposed workshop in the theory of finite groups, building theory, Kac-Moody theory, and geometric group theory. As this workshop brings international experts to the UK, researchers in the UK working in these areas will particularly benefit from this opportunity of discussion and collaboration. We expect that the proposed workshop will help to further strengthen and increase the UK's competitiveness in these areas of mathematical research. The subject of this workshop is in the realm of theoretical mathematics. As with most blue-sky research in fundamental science, immediate economic impact is unlikely. Of course, much of modern society's knowledge and many breakthroughs that make today's life easier and more rewarding are the results of such fundamental research.