Groups and Geometries

Abstract

The workshop Groups and Geometries was one of a series of Oberwolfach workshops on this topic which has taken place every 3 years for some time. It focused on algebraic and finite groups, their interactions with the geometry of buildings, and applications.

A particular highlight of the meeting was a celebration of the recent award of the Abel Prize jointly to John Thompson and Jacques Tits, two of the great pioneers of modern group theory and geometry, and both leading participants at many Oberwolfach meetings. The celebration took the form of two special lectures, given on the Tuesday evening. In the first, Bernd Fischer gave some personal recollections about Thompson, and spoke about his enormous influence on the development of finite group theory. The second lecture was given by Richard Weiss, who described some of the revolutionary innovations of Tits in the geometrical aspects of group theory, and also told some stories illustrating how Tits inspired people through his warmth and sense of humour.

There were 45 participants and 26 talks. These were on three main inter-related themes: buildings and their relationship with algebraic groups; structure of finite groups; and applications. Particularly pleasing was the participation of a substantial number (more than 10) of young researchers, several of whom – Alice Devillers, Silvia Onofrei, Rebecca Waldecker, Pierre-Emmanuel Caprace, Ralf Gramlich, Harald Helfgott and Nikolay Nikolov – gave talks. This demonstrates the attractiveness of the field.

The conference showed that the theories of buildings, algebraic groups, and finite simple groups and their geometries are very active areas with a great deal of interaction between them and also with other areas. People from these different areas were brought together, and their interaction was indeed very lively. The conference stands in the tradition of very successful meetings on Groups and Geometries at Oberwolfach.