Theoretical Statistics and Mathematics Unit, ISI Delhi

October 7, 2015 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Indrava Roy,
Indian Statistical Institute, Delhi

Title:
Baum-Connes conjecture and Atiyah-Patodi-Singer spectral invariants

Abstract of Talk

The Atiyah-Singer index theorem describes a deep relation between the analytic and geometric-topological properties of a compact smooth manifold. Further development of the theory by Atiyah, Patodi and Singer established the existence of certain spectral invariants which are again intricately related with the underlying geometry.

The development of K-theory and K-homology- its dual theory- are an integral part of this story and lead Baum and Connes to formulate their conjecture, which can be seen as a far-reaching generalization of the Atiyah-Singer index theorem and has several important consequences in analysis and geometric topology, most notably the Novikov conjecture.

In this talk, we shall describe both these theories and investigate how they are related, in particular through the so-called rho-invariants.