The spectral shift function and the Witten index
We survey the notion of the spectral shift function of two operators and recent progress on its connection with the Witten index. We begin with classical definitions of the spectral shift function E(.;H2,H1) under various assumptions on the pair of operators (H2,H1) in a fixed Hilbert space and then discuss some of its properties. We then present a new approach to defining the spectral shift function and discuss Krein's Trace Theorem.