This award will support a conference on the combinatorics of structures coming from algebras and groups of Lie type. These structures include Lie groups, Lie algebras, quantum groups, p-adic groups, real reductive groups, finite groups of Lie type, reflection groups, and fundamental groups of configuration spaces.
The objective is to hold a 6-day conference, hosted by the University of Wisconsin, Madison, in order to foster discussions among current and future researchers working on the combinatorial structures that arise in the study of symmetry and its related mathematics. The meeting will establish focus and promote research on the main combinatorial problems in an area that has had an enormous impact on particle physics, the study of crystals in chemistry, and mathematical research ever since the early work of mathematician Issai Schur and physicist Hermann Weyl. Its continuing vitality is evidenced by much current activity, and it is expected to play a prominent role in mathematics throughout the next decade. Because leaders in this area rarely claim to be from the same mathematical discipline, research is being carried out by "pure" algebraists, combinatorialists, topologists, analysts, mathematical physicists, algebraic geometers, and number theorists. The goal of this conference is to bring these diverse experts together and to focus their discussions on the basic questions: "What is the combinatorics controlling fundamental structures related to symmetry, and what role does it play in algebra, topology, analysis, physics, geometry, and number theory?" The plan is to have 20 to 22 one-hour talks on different aspects of these subjects, with sufficient free time between talks for informal discussion and collaboration. It is expected that between 100 and 125 participants will attend the meeting. Special effort will be made to support the participation of graduate students and recent Ph.D.'s. These young mathematicians will be encouraged to bring their reprints and preprints for the "buffet" of preprints, which will permit browsers to sample their work. Also, each of the young participants will be paired with a senior mathematician having closely related research interests, who will serve as a mentor during the conference. The educational advantages of pairing young and experienced researchers will positively impact the careers of young mathematicians, just as the "preprint buffet" will help to publicize their work.
