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MSRI/Evans Lecture: Topological cyclic homology January 27, 2014 (04:00 PM PST - 05:00 PM PST)
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Location: 60 Evans Hall
Speaker(s) Lars Hesselholt (Nagoya University)
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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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