Regularised traces and Getzler’s rescaling

20.11.2020, 11:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Sylvie Paycha (Uni Potsdam)

Inspired by Gilkey's invariance theory,  Connes' deformation to the normal cone and Getzler's rescaling method, we single out a class of geometric operators among pseudodifferential operators acting on sections of a class of natural vector bundles, to which we attach a rescaling degree.
This degree is then used to express regularised traces of geometric operators in terms of a rescaled limit of Wodzicki residues. When applied to complex powers of the square of a Dirac operator, this amounts to expressing the index of a Dirac operator in terms of a local residue  involving the Getzler rescaled limit of its square.