The residue formula and Connes' trace theorem

Abstract:

In 1989, Alain Connes showed in his famous trace theorem that the notion of integration on a compact manifold $M$ is preserved in noncommutative geometry using a class of singular traces on pseudo-differential operators of order $-d$ on $L_2(M)$. However, when $M$ is only locally compact, technicalities ensue. In this talk, we discuss how the use of residue theorems can overcome these technicalities. Joint work with D. Potapov, F. Sukochev and D. Zanin.