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Homological stability of moduli spaces via E_k-algebras

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

I will present some homological stability results for diffeomorphism groups of the manifolds $W_{g,1}:=D \# (Sn \times Sn){\#g}$ and spin mapping class groups of surfaces.  The proof of these results is based on the cellular E_k algebra method introduced by Galatius—Kupers—Randal-Williams, which enables the use of various homotopy theoretic tools to study homological stability.   I will explain the main steps of this method and how it applies to both diffeomorphism groups and spin mapping class groups, focusing on some underlying ideas and computations that can also be applied in more general contexts. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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