Noncommutative Geometry Seminar

I explain how the scalar curvature of

the conformally perturbed noncommutative 4-torus can

be computed by making use of a noncommutative residue.

This method justifies the remarkable cancellations that

occurred when the curvature was computed previously in a

joint work with M. Khalkhali, using the rearrangement lemma.

Furthermore, it allows to recover the 2-variable function

in the formula as the sum of a finite difference and a

finite product of the 1-variable function. The

simplification of the curvature formula for the dilatons

associated with an arbitrary projection and an explicit

computation of the gradient of the analog of the

Einstein-Hilbert action will be outlined.