May 26, 2018

Ontario Non-Commutative Geometry Seminar

November 5 & 12 , 2002 -- 2:00 pm
Xiaodong Hu, University of Toronto

The Connes-Moscovici local index formula and transversally elliptic operators

(Continued from previous talks about zeta functions and noncommutative residues for pseudo-differential operators.)

We introduce the notion of spectral triple and explain a general local index theorem of Connes-Moscovici (1995, GAFA) for spectral triples. The zeta function method plays an important role here. The noncommutative residue was extended by Connes and Moscovici to a general context for spectral triples.

As an application of the general theorem, we introduce the spectral triples for
transversally elliptic operators. The dimension spectrum for such a spectral triple consists of rational numbers, with non-simple poles but bounded multiplicities (rare in other known examples). The index of such a spectral triple index is decided by its full symbol (simply put, it is computable).

This talk is expository, with follow-ups to explain more details.

For more details on the thematic year, see Program Page