Abstract: The noncommutative two torus $A_theta$ equipped with a general complex structure and Weyl conformal factor, is a noncommutative Riemannian manifold where the metric information is encoded in the Dirac operator $D$ of a spectral triple over this C*-algebra. In a recent joint work with M. Khalkhali, we computed a local expression for the scalar curvature of $A_theta$. This was achieved by finding an explicit formula for the value at the origin of the analytic continuation of the spectra zeta function $\Zeta_a(s) := Trace (a|D|^{-s}) (Real(s) >> 0)$ as a linear functional in $a \in A_theta$ . This local expression was also computed by Connes and Moscovici independently. In this talk, I will explain how they have used this local formula and variational methods to compute the determinant of the Laplacian D2 on $A_theta$.