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A multilinear approach to the restriction problem with applications to geometric measure theory, the Schrödinger equation and inverse problems

Project description

Multilinear restriction analysis applied to the Schrödinger equation

The Fourier transform is a mathematical operation that can be used to decompose a function into its constituting frequencies, making it essential in many areas of physics and engineering. An important open problem in harmonic analysis is Stein's Fourier restriction conjecture, which attempts to interpret the situation after many frequencies have been discarded. The recently discovered multilinear estimates have rapidly become a key tool in Fourier restriction theory. Funded by the Marie Skłodowska-Curie Actions programme, the RESTRICTIONAPP project aims to further develop multilinear restriction estimates, with explicit dependence on transversality, and apply them to the Schrödinger equation, to inverse problems as well as to several problems in geometric measure theory.

Objective

The Fourier restriction conjecture, one of main open problems in harmonic analysis, has deep connections with problems in a variety of different fields of mathematics. The aim of this proposal is to further develop the multilinear approach in restriction theory and apply it to several problems in geometric measure theory, the Schrödinger equation and inverse problems.

In order to develop this proposal, the Experienced Researcher will join the harmonic analysis group at ICMAT under the supervision of one of its permanent researchers, Keith Rogers, an ERC grant awardee. The host group has extensive experience in the application of harmonic analysis techniques to inverse problems and geometric measure theory, among others. The scientific training strategy of this proposal consists in the assimilation of the techniques of geometric measure theory and inverse problems. While the Researcher is experienced in restriction theory and dispersive equations, as evidenced by his contributions to the field, it is the combination of this prior knowledge with the proposed scientific training that is needed for the successful development of this proposal.

This MSC fellowship will achieve a variety of positive outcomes: boosting the convergence of distinct research fields and collaborative networks, producing a synergy with the ERC Starting Grant recently held by the Supervisor, and diversifying the fellow’s mathematical knowledge, ultimately strengthening him as an independent researcher.

Fields of science

Coordinator

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Net EU contribution
€ 172 932,48
Address
Calle serrano 117
28006 Madrid
Spain

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Region
Comunidad de Madrid Comunidad de Madrid Madrid
Activity type
Research Organisations
Links
Other funding
€ 0,00