Topology Seminar (Main Talk): Random nilpotent groups

Seminar | October 14 | 4:10-5 p.m. | 3 Evans Hall

 Moon Duchin, Tufts University

 Department of Mathematics

Now-classic results in geometric group theory say that if you begin with a free group and add relators at random, you'll almost surely get a hyperbolic group (in other words, with tree-like geometry). At the other extreme, if you mod out random vectors from a free abelian group, the resulting distribution on abelian quotient groups is pretty well studied by number theorists, topologists, and combinatorialists (each for their own reasons). I'll look at a model in between, where the initial group is free nilpotent, and try to understand the random nilpotent groups that result. First I'll motivate this with a discussion of nilpotent groups and their important role in geometric group theory.