Algebraic Combinatorics Seminar - Michael Borinsky

Title: OutFn, M_gn and renormalized topological field theory

Abstract:

I will report on recent joint work with Karen Vogtmann on the Euler characteristic of Out(F_n) and the moduli space of graphs. A similar study has been performed in the seminal 1986 work of Harer and Zagier on the Euler characteristic of the mapping class group and the moduli​​​​​​​ space of curves. I will review a topological field theory proof, due to Kontsevich, of Harer and Zagier´s result and illustrate how an analogous `renormalized` topological field theory argument can be applied to Out(F_n).