Departmental Colloquium
Benson Farb
University of Chicago
Representation Theory and Homological Stability
Abstract: Tom Church and I were doing some cohomology computations in topology when we discovered what looked like a pattern. After some struggle, we found a language in which to describe this pattern, and called it "representation stability". We started to look around and soon realized that this phenomenon occurs all over the place, from classical representation theory (Littlewood--Richardson and Murnaghan rules, stability of Schur functors), to cohomology of groups (pure braid, Torelli and congruence groups), to Lie algebras, to the study of flag and Schubert varieties, to algebraic combinatorics (the $(n+1)^{n-1}$ conjecture).
The goal of this talk will be to explain representation stability through an example. I will also explain how Church, Jordan Ellenberg and I are applying this theory in order to compute various combinatorial statistics in number theory. I will try to make this talk accessible to first-year graduate students.
Friday November 5, 2010 at 3:00 PM in SEO 636