Speaker: Maxim Braverman, Northeastern University

Date: May 26, 2026

Abstract: In the first part of the talk, I will discuss the semi-classical Weyl law for Schrödinger operators on an arbitrary complete Riemannian manifold, under the sole assumption that the potential grows at infinity.

The second part of the talk concerns joint work with Xianzhe Dai and Junrong Yan, in which we establish a general condition guaranteeing that a classical Weyl law holds on a complete Riemannian manifold. Unlike existing results, we impose no restrictions on the geometry at infinity — such as asymptotic hyperbolicity or asymptotic Euclideanness. Instead, we introduce a geometric-analytic invariant that captures the precise interplay between the geometry of the manifold and both the growth rate and the oscillation scale of the potential. We formulate the condition for the Weyl law in terms of this invariant and demonstrate, through examples, that the condition is optimal.