There will be a conference on finite groups and related areas held at the University of Cambridge on September 27 - 30, 2012. See www-bcf.usc.edu/~guralnic/JGT80 for more details. The conference is timed to mark the 80th birthday of John Thompson. The study of local group theory proved of fundamental importance in the study of finite groups; it has recently resurfaced in the study of fusion systems and related topological ideas. The classification of finite simple groups is having profound influence in a number of areas of mathematics. At the same time, there is considerable amount of work on the revision of the classification, with significant streamlining and new ideas being brought to bear. The connections to algebraic groups have played central role in the study of groups of Lie type, as well as representation theory in the study of groups and algebras. Developments in all these subjects will be discussed at the conference.
Thompson revolutionized group theory, starting in the late fifties and having central influence ever since then. His odd order paper with Feit, his series of N-group papers and other papers of lasting importance introduced new concepts and ideas which played essential role in the monumental achievement in the subject, the classification of finite simple groups. Thompson won a number of awards, including The Fields Medal, The Abel Prize, and the National Medal of Science. The aim of this research conference is to bring together leading researchers and young mathematicians in these areas. The speakers will include Aschbacher, Capdeboscq, Glauberman, Kessar, Liebeck, Malle, Robinson, Serre, Sin, Smith, Tiep and Thompson. It will be an excellent opportunity to discuss recent developments and plan the way forward for the future.
This award was given to fund a conference on Finite Group Theory to be held in Cambridge University. It was held on September 9-11, 2013 at the University of Cambridge. The conference also received funding from the London Math Society, the University of Cambridge and the National Secturity Agency. The conference was also an occassion to celebrate the 80th birthday of John Thompson snd his contributions to group theory, Galois theory and many other areas of mathematics. He has won the Fields, medal, Abel prize, Wolf prize and many other awards. The academic activities of the conference included twelve outstanding talks by some of the top people in the world including J.-P. Serre and Michael Aschbacher. The talks covered a wide range of topics related to the theme of the conference. In particular, many of the talks focused on the proof of the Classification of Finite Simple Groups (first and second generation proofs) and applications of the theorem. The classication theorem is a singular event in the history of mathematics. Its proof encompasses perhaps 15,000 pages and has had applications in many areas of mathemtics including group theory, number theory, algebraic geometry, logic, lattice theory, model theory and cryptography. The talks of Aschbacher, Solomon and Smith were about the ideas in the proof of this amazing theorem and the contributions of John Thompson. Aschbacher, Kessar and Solomon also discussed the quite new ideas involved in studying fusion systems that generalize some of the ideas from so called local group theory. This brings in ideas of algebraic topology as well as group theory and brings new tools to the field. Parts of the classification have been generalized to this context. Malle and Serre gave talks about Galois groups. Tiep, Robinson and Kessar gave talks about some problems in modular representation theory. Capdeboseq talked about subgroups of Kac-Moody group while Glauberman talked about analogs between finite p-groups and Lie algebras. Weiss and Sin talked about various aspects of geometries. Equally importantly in terms of broader impact, it was an opportunity to bring together outstanding senior researchers in the area with postdocs, graduate students and other junior researchers in group theory and related areas. The conference had three main themes. The first was to recall some of the outstanding achievements in group theory and the ongoing progress. The second was to highlight some recent breakthroughs and applications. Thirdly, there has been a resurgence in the study of local group theory in terms of fusion systems. This allows one to use the methods and tools of algebraic topology. The meeting was very successful. There were almost 100 participants from all over the worlds ranging from graduate students to two Fields Medalists (and Abel prize winners). The talks were scheduled so that there was lots of time available for discussions and many collaborations were started. Due to funding from other agencies, there were surplus funds. These were used to fund nine US participants to a meeting at the Banff International Research Station (BIRS) in March 2014. The focus of that workshop was certain fundamental problems in representation theory (using the classification of finite simple groups). The website www.dpmms.cam.ac.uk/Seminars/Conferences/Thompson80 has detailed information on the talks (with abstracts), participants and other information.
