Math Colloquium – Thompson’s group F and geometric group theory

Mathematics Colloquium
Speaker: Professor Sean Cleary, The City College of New York and the CUNY Graduate Center

Abstract: In the early 1960’s Richard J. Thompson discovered a fascinating family of infinite groups in connection with his work in logic. These groups have reappeared in a wide variety of settings, including homotopy theory, measure theory of discrete groups, non-associative algebras, dynamical systems, and geometric group theory. Geometric group theory considers infinite groups as geometric objects, and has been productive in bring tools modeled on differential geometry notions to the discrete settings of countably infinite groups. Thompson’s group F is the simplest known example of a variety of unusual group-theoretic phenomena and has been the subject of a great deal of study. I will describe these groups from several different perspectives and discuss some of their remarkable properties, particularly some unusual aspects of the geometry of their Cayley graphs.