The Arthur trace formula and Weyl laws on GL(2)

Abstract: I will explain the classical Weyl laws on compact Riemannian manifolds, on hyperbolic Riemann surfaces with finite volume and my generalization to arithmetic locally symmetric spaces related to GL(2) over a number field.
The Selberg trace formula and the Arthur trace formula are the main ingredients in the proof. I will explain how to refine the coarse Arthur trace formula via archimedean and non-archimedean harmonic analysis on GL(2).