| DATE: | April 23, 2009 |
| TIME: | 4:30 - 5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Ilya Kapovich, (University of Illinois at Urbana-Champaign) |
| TITLE: | Algebraic rigidity and randomness in group theory. |
The study of finitely generated groups obtained by various kinds random constructions has been an actively developing topic in Geometric Group Theory in recent years. A particularly important application of such probabilistic methods is a result of Gromov proving the existence of a finitely presented group that does not admit a uniform embedding into a Hilbert space. We will discuss a number of results related to algebraic properties of "generic" groups. In particular, we show that random one-relator groups and "generic" finitely presented quotients of the modular group enjoy a strong Mostow-type isomorphism rigidity property and are essentially algebraically incompressible. Applications include counting isomorphism types for several classes of groups given by generators and relators. The talk is based mostly on joint work with Paul Schupp.