A friendly introduction to homology (stability) of algebrasMPIM

by Guy Boyde (Vrije Universiteit)

Monday Jun 29, 2026, 11:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Quantum topology seminar

This talk is about the homological algebra of a class of associative algebras which are often called "diagrammatic". I'll try to give an overview which is approachable regardless of whether you are in rep theory, homotopy theory, or knot theory. First I'll describe how people got interested in these questions: roughly speaking, they were interested in a phenomenon called homological stability, and wanted to know whether it can be done for algebras. I'll try to give an overview of how those results go for the most studied examples: Temperley--Lieb, Brauer, and partition algebras. Second, I'll say something about recent joint work with Boyd, Randal-Williams, and Sroka, where we finish the calculation of the homology of Temperley--Lieb algebras, and find some interesting new patterns. Lastly, time permitting, I'll come back to an elementary question ("are the Temperley--Lieb and planar partition algebras always isomorphic?") and say a few words about work in progress with Dan Graves in this direction.