Workshop on the Extended Family of R. Thompson Groups.

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The proposed project is a workshop, with primary focus the theory of the extended family of R. Thompson groups. The extended family of R. Thompson groups are an important family of (generally) finitely presented simple groups (or, nearly simple) which contain the first known examples of finitely presented infinite simple groups. The theory of this family intersects other areas of mathematics in often surprising and profound ways; providing examples and counterexamples to questions from areas such as logic (R. J. Thompson), solvable and unsolvable problems in group theory (R. J. Thompson and R. McKenzie), homotopy and category theory (P. Freyd and A. Heller), shape theory (J Dydak and H. Hastings), Teichmuller theory and mapping class groups (R. Penner) and various other areas as well.The workshop will serve to both educate new and established researchers on the State of the Art in this dynamic area, as well as highlight some of the many connections between the theory of these groups and other areas of Mathematics. In particular, the workshop will host three mini-courses on the connections of the extended family of the R. Thompson groups to various outward-reaching areas of mathematics. The titles and presenters of these workshops are given below:1) Semigroups, 'etale topological groupoids, C*-algebras, and Thompson groups; Mark V. Lawson.2) Braids, logic and geometric presentations for Thompson's groups; Patrick Dehornoy.3) Thurston's piecewise integral projective groups; Vladimir Sergiescu.The workshop will also host a problem session focussing on these groups and the broader topics associated with them, and will publish summaries of the minicourses and the problem session discussion in a topical research journal.