Homological stability for Temperley-Lieb algebras

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• Rachael Boyd, Cambridge
• Wednesday 17 November 2021, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Many sequences of groups and spaces satisfy a phenomenon called ‘homological stability’. I will present joint work with Hepworth, in which we abstract this notion to sequences of algebras, and prove homological stability for the sequence of Temperley-Lieb algebras. The proof uses a new technique of ‘inductive resolutions’, to overcome the lack of flatness of the Temperley-Lieb algebras. I will also introduce the ‘complex of planar injective words’ which plays a key role in our work. Time permitting, I will explore some connections to representation theory and combinatorics that arose from our work.

This talk is part of the Differential Geometry and Topology Seminar series.

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