Abstract: I will survey on a recent joint work with M. Khalkhali and a paper by Connes and Moscovici on scalar curvature for noncommutative two-tori. The scalar curvature is computed by considering small time heat kernel expansions of the perturbed Laplacian which encodes the metric information of a general translation invariant conformal structure and a Weyl conformal factor on the noncommutative two-torus. There is an equivalent formulation for the scalar curvature in terms of special values of spectral zeta functions. I will also talk about our result on the Gauss-Bonnet theorem for noncommutative two-tori which extends the work of Connes and Tretkoff to the general conformal structures.

Abstract: I will try to discuss how to extend the classical moment maps to the diffeological case, and hopefully some applications to some orbifolds, etc.