Thompson's group at 40 years

January 11 to 14, 2004

at the

American Institute of Mathematics, Palo Alto, California

organized by

Sean Cleary, John Stallings and Jennifer Taback

This workshop, sponsored by AIM and the NSF, will be devoted to understanding Thompson's group F from many different viewpoints, and approaching some open questions about the group.

This workshop will bring together researchers in group theory, category theory and dynamics for a joint approach towards Thompson's group F . We hope especially to facilitate communication between researchers in these differing fields who may view Thomspson's group in quite different ways. Exploring the connections between these viewpoints will lead to new and innovative approaches to some open problems concerning this group.

Thompson's group F has a number of different manifestations. Thompson, while constructing groups with unsolvable word problem, originally discovered F as a group of automorphisms of a free algebra. F, though, can be understood in many different ways. F is the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval, where the slopes are powers of two and the places where the slope changes are dyadic rationals. F has an infinite presentation which allows a convenient set of unique normal forms. F has a finite presentation with two generators and two relators, of lengths 10 and 14. F is the universal example of a group conjugacy idempotent. F is a group of tree pair diagrams where elements are represented by pairs of rooted binary trees. F is the diagram group for one of the simplest presentations of the trivial semigroup.

The main goals for the workshop are

Understanding F from the viewpoints of: category theory, diagram groups, dynamics, foliations, cohomology, branch groups, and metrically.
Discussing open problems for this group. We hope that all participants will come prepared with questions about F which interest them.
Combining the different viewpoints to suggest strategies for solving some open questions.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and there will be ample time between talks for discussions and for work to be done.

Invited participants include M. Bridson, M. Brin, K. Brown, J. Burillo, J. Cannon, S. Cleary, P. DeHornoy, L. DeMarco, D. Farley, W. Floyd, B. Fordham, F. Gardiner, R. Geoghegan, V. Guba, B. Harvey, S. Hermiller, L. Keen, J. Meier, W. Parry, M. Sapir, V. Sergiescu, J. Stallings, M. Stein, J. Taback, and R. Thompson.

The deadline to apply for support to participate in this workshop has passed.

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