Alejandro Uribe

A semi-classical trace formula for Schrödinger operators

AbstractLetSℏ=−ℏΔ+V, withV smooth. If 0<E2<lim infV(x), the spectrum ofSℏ nearE2 consists (for ℏ small) of finitely-many eigenvalues,λj(ℏ). We study the asymptotic distribution of these eigenvalues aboutE2 as ℏ→0; we obtain semi-classical asymptotics for

Spectral statistics on zoll surfaces

\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)}

The Manifold of Compatible Almost Complex Structures and Geometric Quantization

with

The Weyl Quantization and the Quantum Group Quantization of the Moduli Space of Flat SU (2)-Connections on the Torus are the Same

\hat f \in C_0^\infty

Theta functions on the Kodaira-Thurston manifold

, in terms of the periodic classical trajectories on the energy surface