Mathematics

The goal of these lectures is to explain a few of the many developments generated by the the Atiyah-Singer index theorem. After a quick introduction to the Atiyah-Singer formula itself I will pass to families of elliptic operators, to the associated index bundle and to the the index formula for its Chern character.

I will then talk about the Connes-Moscovici higher index formula on Galois coverings, a far reaching generalisation of the family-index-theorem. Finally I will talk about the index theorem on manifolds with boundary and how it can be used in order to define and study interesting and useful geometric invariants (the rho invariants).

No prerequisites are needed, everyone who is interested is invited to come.