Complementing Yuan's previous talk, I will explain a criterion on a pre-cyclotomic commutative ring spectrum R that suffices to construct a pre-cyclotomic structure on topological Hochschild homology relative to R. We are motivated by applications to Floer homotopy theory; our main examples of interest are periodic circle-equivariant complex cobordism (MUP) and a new circle-equivariant version of MU. The technical requirements for this work involve resolution of some interesting questions in the foundations of equivariant stable homotopy theory, which I will also discuss.  This talk describes joint work with Mandell and Yuan.

Online Talk