Bonn Topology Group - Abstracts

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Talk

January 14th 2020
Richard Hepworth (University of Aberdeen, UK): Homological stability for algebras

Abstract

Homological stability is a property of sequences of groups, and states roughly that the groups are increasingly similar the further you go along the sequence. But the homology of a group can be interpreted in a purely algebraic way, as the Tor groups of the group ring. This means that one can try to prove homological stability for arbitrary sequences of augmented algebras, rather than just for sequences of groups. In this talk I will show how this works out in the case of the Iwahori-Hecke algebras, which are deformations of the group ring of the symmetric group, and play an important role in representation theory, knot theory and combinatorics.
The talk will be pitched for topologists, so in particular I will introduce the Iwahori-Hecke algebras in detail.

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