| DATE: | Thursday, March 20, 2003 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Simon Thomas (Rutgers University) |
| TITLE: | Asymptotic cones of finitely generated groups |
If an observer moves steadily away from the Cayley graph of a finitely generated group, then any finite configuration will eventually become indistinguishable from a single point; but he may observe certain finite configurations which resemble earlier configurations. The asymptotic cone is a topological space which encodes all of these recurring finite configurations. Unfortunately the construction of an asymptotic cone involves a number of non-canonical choices, and it was not clear whether the resulting asymptotic cone was independent of these choices. In this talk, partially answering a question of Gromov, I shall consider the question of whether lattices in SL(n,R) have unique asymptotic cones up to homeomorphism. The answer turns out to be very surprising! This is joint work with Linus Kramer, Saharon Shelah and Katrin Tent.