Richard Hepworth: Homology of Algebras with Structure

It is often the case that if an associative algebra admits some kind of "extra structure" then its Hochschild homology also admits some "extra structure".  For example the Hochschild homology of a commutative algebra is itself a commutative algebra.  Recent work of Nathalie Wahl and Craig Westerland investigates this question of "extra structure" in detail, giving several general results and working out many interesting examples.  My talk will explain how to generalise this work to new contexts such as cyclic homology, topological Hochschild homology and topological chiral homology.  The main tool is enriched category theory (which I won't assume any knowledge of).  I will then explain the cyclic case in some detail. This is joint work with Jeff Giansiracusa.