
THEMATIC PROGRAMS 

September 20, 2024  
Ontario NonCommutative Geometry Seminar November 5 & 12 , 2002  2:00 pm

(Continued from previous talks about zeta functions and noncommutative residues for pseudodifferential operators.)
We introduce the notion of spectral triple and explain a general local index theorem of ConnesMoscovici (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 nonsimple 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 followups to explain more details.
For more details on the thematic year, see Program Page