Fuglede's conjecture

Fuglede's conjecture, proposed by the mathematician Bjarne Fuglede in 1974, is a statement in the field of mathematics that relates to the concepts of spectral sets and tiling in Euclidean space. Specifically, the conjecture asserts that: A measurable subset \( S \) of \( \mathbb{R}^n \) can tile \( \mathbb{R}^n \) by translations if and only if it is a spectral set.