|Topic:||Subgroups of random groups|
|Affiliation:||University of Chicago; Member, School of Mathematics|
|Date:||Monday, October 19|
|Time/Room:||2:00pm - 3:00pm/S-101|
What can you learn about a group from a presentation? Sometimes very little; almost every interesting problem about groups given by (finite) presentations is unsolvable in full generality. But if one asks about *typical* groups - so-called "random" groups (in various models) - then the situation is much better, and one can usually tell a lot from a presentation. In particular, it turns out that random groups contain many familiar and beautiful subgroups, and these can be found and certified easily from the presentation. Some of this is joint work with Alden Walker, and some with Henry Wilton.