Fuglede's conjecture

Proposed by Danish mathematician Bent Fuglede in 1974

Fuglede's conjecture

1. (mathematics) The conjecture that every domain of ${\displaystyle \mathbb {R} ^{d}}$ (i.e. subset of ${\displaystyle \mathbb {R} ^{d}}$ with positive finite Lebesgue measure) is a spectral set if and only if it tiles ${\displaystyle \mathbb {R} ^{d}}$ by translation.