Unwinding the Tate diagonal

Tyler Lawson, University of Minnesota

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

Some of the most effective methods for computation in algebraic K-theory use its relationship to another construction, called TC for topological cyclic homology. The construction of TC makes heavy use of a structure in stable homotopy theory called the Tate diagonal that is not present in algebra. In this talk I will discuss some conceptual background behind the Tate diagonal and how it can be generalized to structures beyond the Hochschild complex. As an application, we discuss how a spectral sequence of Lipshitz-Treumann, attempting to relate the Hochschild homology of a differential graded algebra to a "doubled" variant of it, is actually computing a localized version of topological Hochschild homology.