Abstract: A Fourier uniqueness pair is a pair of subsets A, B of Euclidean space such that any sufficiently nice function can be recovered from its restriction to A and restriction of its Fourier transform to B. Although this notion is related to several classical results in harmonic analysis, the first constructions of uniqueness pairs with both A and B discrete closed sets were obtained only recently, and these constructions played a crucial role in the sphere packing and energy minimization problems in 8 and 24 dimensions. I will talk about some recent progress on Fourier uniqueness pairs, including both analytic and number-theoretic constructions. If time permits I will also discuss conjectural applications to sphere packing and energy minimization problems in dimensions other than 8 and 24.
Fourier uniqueness pairs, interpolation, and extremal problems
29.01.2025 15:15 - 16:15
Location: