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MSRI/Evans Lecture: Topological cyclic homology (Evans Hall, UC Berkeley)

Introductory Workshop: Algebraic Topology January 27, 2014 - January 31, 2014

January 27, 2014 (04:10PM PST - 05:00PM PST)
Speaker(s): Lars Hesselholt (Nagoya University)
Location: UC Berkeley, 60 Evans Hall
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Abstract

Topological cyclic homology is a topological refinement of Connes' cyclic homology. It was introduced twenty-five years ago by Bökstedt-Hsiang-Madsen who used it to prove the K-theoretic Novikov conjecture for discrete groups all of whose integral homology groups are finitely generated. In this talk, I will give an introduction to topological cyclic homology and explain how results obtained in the intervening years lead to a short proof of this result in which the necessity of the finite generation hypothesis becomes transparent. In the end I will explain how one may hope to remove this restriction and discuss number theoretic consequences that would ensue.

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