Loops, groups, and twists - the role of K-theory in mathematical physics

Abstract: While K-theory has its origins in Grothendieck's formulation and proof of his version of the Riemann-Roch theorem, it now plays a significant role in many diverse branches of mathematics: It provides a fundamental example of a cohomology theory, and it is one of the most important invariants of C*-algebras. In the first half of the talk, I will define the K-groups and discuss some of their applications. In the second half, I will concentrate on equivariant twisted K-theory, which is related to the representation theory of loop groups and the geometry of two-dimensional quantum field theories by a theorem of Freed, Hopkins, and Teleman. I will finish with an outline of joint work with D. Evans, in which we study generalizations of this work to higher twists.

algebraic topology

Audience: researchers in the topic

Online algebraic topology seminar

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