Permutation Groups (09w5030)


(University of Southern California)

(University of Western Australia)

Jan Saxl (University of Cambridge)

(University of Muenster)


The Banff International Research Station will host the "Permutation Groups" workshop next week, July 19 - July 24, 2009.

The group of permutations of a finite set is one of the most important examples of a finite group. Indeed, one of the most ancient theorems in the subject tells us that every group is a subgroup of a permutation group. In the last two decades, there has been enormous progress in the theory. More importantly, permutation groups are a fundamental way to apply the group theory machinery to many problems in number theory, algebraic geometry and logic. For example, these ideas were used to answer Mark Kac's question about hearing the shape of a drum. More recently, there has been much progress related to expander graphs (with connections to computer networks) coming out of group theory.

The flow goes both ways. Techniques and questions from other areas of mathematics have led to breakthroughs in permutation groups. This workshop will bring together both experts and outstanding young people in the field and related areas.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).