6 problems

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…

Anantharaman–Koch–Nonnenmacher's conjecture. In all dimensions, the optimal lower bound for the entropy of semiclassical measures of quantum cat maps is half the topological entrop…

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 $M$ be a compact Riemannian manifold with geodesic flow, and let $bc_\gamma$ denote the invariant singular measure supported on a periodic geodesic $\gamma$. A semiclassical me…

Let $\{\psi_\Bbbk\}_{\Bbbk=1}^{\infty}$ be a sequence of eigenstates, with associated measures $d\mu_\Bbbk=W_\Bbbk(x,\xi)\,dx\,d\xi$ on the classical phase space. A limiting semicl…