Finding a representative for the Chern character of the index bundle (Alex Taylor)
A big problem in index theory is to establish index formulas for families of Diract operators, which amounts to finding a suitable representative for the Chern character of the K-theoretic “index bundle” of the family.
I’ll introduce the index bundle and explain Quillen’s approach to this problem using superconnections, where the index formula is deduced from a transgression formula appearing in Chern-Weil theory.