Skip to main content

Hochschild reading seminar

The seminar will be divided between a lecture series/learning seminar on Hochschild homology and its various generalizations, and talks given by invited speakers. Please write us about speakers you would like to invite to the seminar. Please also write us if there is a particular topic you would like to speak or hear about in the Hochschild talks. Here is a list of talks that we would like to have in the seminar:


  • Hochschild homology and the free loop space: HH of group rings

  • Basic results: B-operator, Hochschild-Kostant-Rosenberg

  • Cyclic homology and homotopy orbits/equivariant homology

  • K-theory and the Dennis trace

  • The goodwillie isomorphism theorem

  • Topological Hochschild homology

  • Algebraic K-theory of spaces and automorphisms of manifolds

  • TC and calculations for F_p

  • The cyclotomic trace and assembly maps

  • The Dundas-McCarthy theorem, calculations of A(pt)

  Literature: Loday: Cyclic homology, Dundas-Goodwillie-McCarthy: The local structure of algebraic K-theory, Madsen: K-theory and traces, Nikolaus-Scholze: On topological cyclic homology, Waldhausen: Algebraic K-theory of spaces. The goal is that every talk should explain or calculate some interesting example. There are various ways that this can continue or be elaborated. Some suggestions are: - connections to string topology - The Farrell-Jones and Novikov conjectures - the de Rham-Witt complex and p-adic Hodge theory - foundational aspects on infinity categories or equivariant stable homotopy - Functor calculus and the proof of the Dundas-MacCarthy theorem Suggestions are very welcome.