Oberseminar Geometrie und Topologie
(run by Sebastian Hensel, Christian Lange, and Bernhard Leeb)
The seminar takes place on Thursdays, 16:15, virtually via zoom.If you want to participate, please send a quick email to Sebastian Hensel to be added to the mailing list, and you will receive invitations and zoom links.

May 6th, 2021: Richard Webb (Manchester): How nonpositively curved is the mapping class group?
Abstract: In general, mapping class groups are not CAT(0) but one is still interested in finding nonproper yet cocompact actions on CAT(0) spaces. We will show that, in general, the arc complex admits no CAT(0) metric with finitely many shapes. In particular there is no finiteindex subgroup of the mapping class group that preserves a CAT(0) metric on the arc complex. The hex theorem from combinatorics plays a role in the proof. The analogous statements are true for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups. I will give background and motivation, and some connections of the work with other areas of algebra and topology. 
May 27th, 2021: Alessandro Sisto (HeriotWatt): What does a generic 3manifold look like?
Abstract: I will discuss two constructions of "random" 3manifolds, namely Heegaard splittings and mapping tori where the gluing map is chosen using a random walk on a mapping class group. As it turns out, in both cases one obtains hyperbolic manifolds with asymptotic probability 1. I will give a brief overview of further geometric properties of these manifolds, and then focus on a deterministic result on Heegaard splittings, joint with Peter Feller and Gabriele Viaggi, that applies to random Heegaard splittings. 
June 10th, 2021: Jose Andres Rodriguez Migueles (LMU) Volumes associated to periodic orbits of the geodesic flow on the Modular surface
Abstract: Closed geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle. The isotopy class of any periodic orbit can be considered as a knot in a 3manifold. The complement of those knots is always a hyperbolic 3manifold, and hence has a welldefined volume. We show that there exist sequences of closed geodesics for which this volume is bounded linearly in terms of the period of the geodesicâ€™s continued fraction expansion. 
June 17th, 2021: Christian Lange (LMU)