Noncommutative geometry and spectral flow

The goal of this talk is to explain the connection of spectral flow to K-theory/K-homology, and to introduce the p-summable integral formula for spectral flow. Recall that spectral flow (introduced in the talk on Nov. 1st) measures, for a path of Breuer-Fredholm self-adjoint operators, the net amount of spectrum which crosses zero in the positive direction as you move along the path. In a specific context, the spectral flow can be used to calculate the index pairing between K-theory and K-homology. I will start with a bird’s eye view of K-theory and K-homology, leading up to the main result of the talk, which is the p-summable integral formula for spectral flow.