**Monday 21 March 2022**

**15:00–16:30***

**Jan Steinebrunner (University of Cambridge)** — *Filtering the modular surface operad*

I will explain how the moduli spaces of surfaces assemble into a graded modular operad whose envelope is the surface category studied by Galatius-Madsen-Tillmann-Weiss. For any graded modular operad there is a filtration by genus, which in this case yields a filtration of MTSO_{2}. The associated graded can be described in terms of the curve complex.

This leads to a spectral sequence with E^{1}-page the (dualised) unstable homology of mapping class groups and which converges to the spectrum homology of MTSO_{2}. As a computational consequence, we will see that the top-dimensional homology group H_{14}(𝔐_{5}), which was shown to be non-zero by Chan-Galatius-Payne, has at most rank 2.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.