Fourier interpolation pairs and their applications, Maryna Viazovska (Ecole Polytechnique Fédérale de Lausanne)

Lieu : M3 Salle Duhem Oratrice : Maryna Viazovska Affiliation : Ecole Polytechnique Fédérale de Lausanne Dates : Mardi, 24 mai, 2022 - 10:30 - 11:30 Titre: Fourier interpolation pairs and their applications Résumé: This lecture is about  Fourier uniqueness and Fourier interpolation pairs, some explicit constructions of such pairs and their applications. Suppose that we have two subsets X and Y of the Euclidean space. Can we reconstruct a function f from its restriction  to the set X and the restriction of its Fourier transform to the set Y?  We are interested in the pairs (X,Y) such that the answer to the question above is affirmative. In this talk I will give an overview of recent progress on explicit constructions and existence results for Fourier interpolation pairs and corresponding interpolation formulas. Also I will try to convince you that explicit Fourier interpolation is a useful gadget in solving optimization problem and analysing  differential equations.