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Texas A&M University
Mathematics

Noncommutative Geometry Seminar

Date: November 11, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Nigel Higson, Penn State University

  

Title: The Oka principle and Novodvorskii’s theorem

Abstract: In the early days of Banach algebra K-theory, Novodvorskii proved that the Gelfand transform for any commutative Banach induces an isomorphism in Banach algebra K-theory. This is a version of the Oka principle in several complex variables, which identifies equivalence classes of structures, including vector bundles, in the holomorphic and continuous categories in a variety of contexts. Since the Oka principle has long been proposed as a mechanism to understand and indeed prove the Baum-Connes conjecture, Novodvorskii’s theorem continues to be of interest in noncommutative geometry. I shall give a more or less self-contained proof of Novodvorskii’s theorem, along with a rough sketch of possible future extensions into the noncommutative realm. This is joint work with Jacob Bradd.

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