Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page