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Cellular E_k-algebras and homological stability

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HHH - Homotopy harnessing higher structures

I will explain recent joint work with S Galatius and A. Kupers in which we use the notion of cellular E_k-algebras and their derived indecomposables to study homological stability for things such as mapping class groups, automorphism groups of free groups, or general linear groups. Using these tools also suggests new types of results in homological stability, such as a second-order form of stability. In this talk I will suppress the details specific to each case, and instead focus on the general calculational aspects of the homology of cellular E_k-algebras with few cells.

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

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