Mathematics Department Colloquium: On topological cyclic homology

Colloquium | March 16 | 4:10-5 p.m. | 60 Evans Hall

 Thomas Nikolaus, MPIM Bonn

 Department of Mathematics

We first introduce/recall the classical Hochschild homology groups and give some examples that illustrate the behaviour in different characteristics. Then we explain the variants and developments of Hochschild homology that eventually lead to the definition of topological cyclic homology by Bökstedt, Hsiang and Madsen. They invented topological cyclic homology to study algebraic K-theory but in recent years it has become more and more important as an invariant in its own right.

The main result that we present is a new formula for topological cyclic homology which is joint work with P. Scholze. If time allows we explain consequences and possible further directions.