Title: The Cyclotomic Hodge Filtration
Speaker: Saul Glasman, MIT
Abstract: In the 80s, many mathematicians independently defined a filtration on the Hochschild homology of a commutative algebra A that recovers the Hodge filtration of the de Rham complex of A in the case where A is a smooth Q-algebra. The subject of this talk is a refinement of this to a filtration by spectra of the topological Hochschild homology of a commutative ring spectrum. I'll discuss why one would want such a thing; in particular, similar objects are implicated in the study of special values of L-functions. Then I'll talk about how to construct it, and if time permits, how to lift it to a filtration of topological cyclic homology using techniques of equivariant stable homotopy theory.