Noncommutative Geometry Seminar

The flat geometry of noncommutative two tori can be
conformally perturbed by a Weyl factor, and one can compute the
local geometric invariants of these C*-algebras, such as scalar
curvature, by employing Connes' pseudodifferential calculus to find
explicit formulas for the heat coefficients of the Laplacian associated
with the curved metric. A purely noncommutative feature is the appearance
of a modular automorphism in the computations and final formulas.
In this talk, I will explain my joint works with M. Khalkhali on this
type of computations and the extension of the Gauss-Bonnet theorem of
Connes and Tretkoff to general translation-invariant conformal structures
on noncommutative two tori.