4 problems

Extremal-eigenstate convergence conjecture. If

Open-baker semiclassical-measure conjecture. All long-living semiclassical measures are supported on $\overline{\Gamma_+}$, and almost all long-living eigenstates are non-diffracti…

Let $(M,g)$ be a compact manifold of negative curvature without boundary, and let $(u_n)_{n\geq 1}$ be any orthogonal eigenbasis of the Laplacian. A semiclassical measure is a weak…

Let $M$ be a compact complex hyperbolic quotient, and let $\mu$ be a semiclassical measure, meaning the semiclassical limit of a sequence of Laplacian eigenfunctions on $M$. Its su…