THE OKA PRINCIPLE AND A K-THEORETIC PERSPECTIVE ON THE LANGLANDS CLASSIFICATION

The Oka principle in complex geometry asserts that continuous structures in a variety of contexts, including vector bundles on polynomially convex sets, carry unique holomorphic structures, up to isomorphism.  The Oka principle fits naturally into K-theory, and it has long been proposed as a mechanism to understand cases of the Baum-Connes conjecture.  I shall explain how in the case of real reductive groups it may be combined with the Langlands classification to produce an interesting new perspective on the Connes-Kasparov isomorphism.  This is joint work with Jacob Bradd. 

https://www.youtube.com/watch?v=J8IXQGpXtnQ