Do high-energy quantum states on a chaotic manifold always spread out evenly, or can some cling to classical periodic orbits? Proved for arithmetic surfaces (2006); open in general.
The Problems
Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.
Tagged homogeneous-dynamics — 1 entry. Clear