Pólya’s eigenvalue conjecture
Does the area of a planar region impose a sharp lower bound on every Dirichlet vibration frequency, rather than only on high frequencies in the limit?
Waves and spectra
Vibration frequencies, high-frequency wave patterns and reconstruction from frequency information.
Subjects: Analysis and dynamics · Differential equations
Problems in this collection
3 problemsQuantum unique ergodicity conjecture
Must every sequence of increasingly high-frequency waves spread uniformly in phase space on a connected compact manifold of negative curvature and dimension at least two?
Bochner–Riesz conjecture
How much smoothing of a spherical frequency cutoff guarantees bounded Fourier reconstruction in higher dimensions?