Some applications of filtered and graded $THH$

Speaker: Liam Keenan – University of Minnesota

Abstract: One natural invariant associated to a ring spectrum R is its topological Hochschild homology. If $R$ admits a multiplicative filtration or grading, then these both prolong to $THH(R)$ inducing a “filtered” or “graded” cyclotomic structure. In this talk, I’ll try to explain this point of view and survey some applications, highlighting the case of the May filtration and the $THH$ of a twisted group ring.