Algebra/Topology Seminar 20112020

Speaker: Maxime Ramzi

Title: A multiplicative comparison of MacLane homology and topological Hochschild homology

Abstract: In 92, Pirashvili and Waldhausen proved that MacLane homology
and topological Hochschild homology of a given ring R were isomorphic.
However, their proof only works at the level of homology, and does not say
anything about the multiplicative structure of these two invariants in the
case of a commutative ring.
In joint work with Geoffroy Horel, we lift this comparison to a comparison
of spectra, and we show that it is actually a symmetric monoidal
comparison in the infinity-categorical sense, building on work of
Johnson-McCarthy and a construction of Richter.

I will briefly present the objects appearing in this statement, some of
the previous work around this question, and sketch the proof of our