## Geometry Seminar - Abstracts

### Talk

Tuesday 28 January 2020, 15:30-16:30 in HG02.802

**Michael Borinsky** (NIKHEF)

*Renormalized topological field theory and the Euler characteristic of
Out(F_n) *

### Abstract

I will report on recent joint work with Karen Vogtmann on
the Euler characteristic of \(\operatorname{Out}(F_n)\) 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 an d
Zagier's result and illustrate how an analogous 'renormalized'
topological field theory argument can be applied to
\(\operatorname{Out}(F_n)\).

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