Skip to main content
European Commission logo print header

Fourier Interpolation and Extremal Problems

Obiettivo

In 2006 Cohn and Kumar have conjectured that the A2 lattice is universally optimal, meaning that it has the lowest potential energy among all configurations of the same density for all completely monotone potentials. This conjecture has several very important corollaries. Among other consequences, it is known that it implies a positive solution to the 2D crystallization problem, a major unsolved problem coming from materials science, and it also implies a conjecture on the emergence of the triangular lattice of Abrikosov vortices in the Landau-Ginzburg theory of superconductivity.

Recently, the 8 and 24-dimensional cases of the Cohn-Kumar conjecture have been positively resolved using novel interpolation formulas for radial Schwartz functions. This formula recovers a radial function from the data of it and its Fourier transform on a discrete set of radii, and its construction uses classical modular and quasi-modular forms.

In this project we will prove a significant generalization of these interpolation formulas with a view towards applications in extremal problems in Fourier analysis. To prove these formulas we will develop new analytic and numerical techniques for solving certain types of functional equations in one complex variable. Finally, based on these proposed interpolation formulas we will give a refinement of the Cohn-Kumar conjecture in dimension 2 and use it to attack the full conjecture in this case.

Parole chiave

Meccanismo di finanziamento

HORIZON-ERC - HORIZON ERC Grants
æ

Coordinatore

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Contribution nette de l'UE
€ 1 158 000,00
Indirizzo
Rue michel ange 3
75794 Paris
Francia

Mostra sulla mappa

Regione
Ile-de-France Ile-de-France Paris
Tipo di attività
Research Organisations
Collegamenti
Altri finanziamenti
€ 0,00