April 17, 2014

Ontario Non-Commutative Geometry Seminar

October 1, 2002 -- 2:00 pm
Xiaodong Hu, University of Toronto
Residues of zeta functions and the index theorem

One way to understand the Atiyah-Singer index theorem is through spectral analysis. The index can be described in terms of the residues of certain zeta functions, which are defined as the traces of certain operators involving complex powers of the given elliptic (pseudo-)differential operator. The zeta functions arising in this way are analogues of the classical Riemann zeta function.

In this series of talks, first we will present the classical results (Seeley et al.) on expressing the residues of the zeta functions in terms of local data such as symbols. Then we will illustrate the generalization of this idea to the Chern-Connes character in non-commutative geometry. The main goal is to explain the Connes-Moscovici local index formula (1995) for spectral triples. Finally recent work by the speaker will be presented, which applies the Connes-Moscovici local index formula to give index formulas for transversally elliptic (pseudo-)differential operators.

For more details on the thematic year, see Program Page