Scalar Curvature for the Noncommutative Two Torus

lecturer: Javad Golipour Seyyedkheili

Abstract: We introduce the spectral triple for the noncommutative two torus. By
Connes' reconstruction theorem it is the counterpart of the classical torus
from spin-Riemannian geometry. The metric aspects of this spectral triple
are encoded by two parameters, the complex structure  representative of a
conformal class and the Weyl factor given by a positive invertible element
corresponding to a conformally perturbed metric. The ideas and methods
of pseudo dierential calculus and asymptotic expansion of the heat kernel
of the laplacian are applied to the spectral triple to get a local formula for
the scalar curvature. This is done by putting s = 0 in the zeta functional.