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Character Theory and Tempered Cohomology

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 28, 2019 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Jacob Lurie (Harvard University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • K-theory

  • homotopy theory

  • algebraic geometry

  • character theory

  • formal groups

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

11-Lurie

Abstract

Complex K-theory is a generalized cohomology theory introduced by Atiyah and Hirzebruch, which associates to each finite cell complex X the Grothendieck group KU(X) of complex vector bundles on X. However, it also admits a purely algebraic description which makes no mention of vector bundles: it is the complex-oriented cohomology theory associated to the multiplicative formal group over Spec(Z). In this talk, I'll discuss a variant of this algebraic picture which can be used to recover equivariant complex K-theory (as well as equivariant elliptic cohomology), and explain its relationship with the classical character theory of finite groups and various generalizations thereof.

Supplements
Asset no preview Notes 804 KB application/pdf Download
Video/Audio Files

11-Lurie

H.264 Video 873_26330_7687_11-Lurie.mp4
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