Abstract

The Local Index Formula of Connes and Moscovici (GAFA 1995) is among the deepest results of noncommutative geometry. The theorem has much pedagogical value as well since even an understanding the statement of the theorem requires a knowledge of various central topics in noncommutative geometry: K-theory, K-homology, cyclic cohomology, Connes-Chern character, index theory, elliptic pseudodifferential operators and their zeta functions, Weyl's law and the Dixmier trace. The theorem is expected to play an even more important role in coming years in noncommutative geometry and its applications, specially to high energy physics. In this series of 8 lectures I plan to cover all the basic ingredients of the theorem and give a rather detailed proof of it.