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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

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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.

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