# Algebra/Topology Seminar

Speaker: Michael Borinsky

Title: The Euler characteristic of Out(Fn) and renormalized topological field
theory

Abstract: I will report on ongoing joint work with Karen Vogtmann on the topology of Out(Fn) and the moduli space of graphs. The first part of this work settled a 1987 conjecture on the Euler characteristic of Out(Fn) and indicates the existence of large amounts of homology in odd dimensions. 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(Fn). Moreover, I will report on very recent results on the integer Euler characteristic of Out(Fn) and its growth rate which prove the existence of large amounts of unexplained homology in odd dimensions.