at the

American Institute of Mathematics, Palo Alto, California

organized by

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.

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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