# Geometry and Topology Seminar

Current contact: Dave Futer or Matthew Stover

The Seminar usually takes place on Wednesdays at 2:30 PM in Room 617 on the sixth floor of Wachman Hall.

• Wednesday February 14, 2018 at 14:45, Wachman 617
Moduli of Curves: from GT theory to Arithmetic Geometry

Benjamin Collas, Bayreuth

The goal of Grothendieck-Teichmüller theory is to lead an arithmetic study of the moduli spaces of curves via their geometric fundamental group. Once identified to the profinite orbifold fundamental group, the latter provides a computational framework in terms of braid and mapping class groups.
While the classical GT theory, as developed by Drinfel'd, Lochak, Nakamura, Schneps et al., essentially deals with the schematic or topological properties of the spaces at infinity'', the moduli spaces of curves also admit a stack or orbifold structure that encodes the automorphisms of curves. The goal of this talk is to show how fundamental group theoretic properties of the mapping class groups and Hatcher-Thurston pants decomposition lead to orbifold arithmetic results, then to potential finer GT groups.
We will present in detail this analytic Teichmüller approach and indicate the essential obstacles encountered, before briefly explaining how they can be circumvent in terms of arithmetic geometry.