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Tuesday, January 27, 2015

**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 give some motivation for this filtration and describe its construction and properties, and then I'll discuss how to lift it to a filtration of topological cyclic homology using techniques of equivariant stable homotopy theory.