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Harmonic Analysis and Differential Equations: New Challenges

Total Cost €


EC-Contrib. €






 HADE project word cloud

Explore the words cloud of the HADE project. It provides you a very rough idea of what is the project "HADE" about.

understand    showing    basic    solved    poorly    principles    preliminary    model    modern    setting    dirac    heart    interaction    despite    behavior    sums    integrals    yet    oscillatory    analytical    parisi    underlying    ups    critical    happens    zero    arguments    extended    harmonic    tools    equation    chaotic    unsolved    equations    forth    cutting    theoretical    behave    mechanics    vortex    turbulence    appeared    corners    estimates    versions    frisch    look    suggest    approximation    hardy    electromagnetic    partial    experiments    hamiltonians    prove    dynamics    relativistic    mit    hamiltonian    filament    framework    polygon    bag    filaments    mathematical    time    physics    discrete    view    theory    conjecture    trigonometric    cauchy    differential    interact    structure    seem    quark    covered    regular    algebraic    isolated    confinement    operator    point    analyze    numerical    carleman    issue    vfe    first    controls    edge    quantum   

Project "HADE" data sheet

The following table provides information about the project.


Organization address
city: LEIOA
postcode: 48940

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Spain [ES]
 Project website
 Total cost 1˙672˙103 €
 EC max contribution 1˙672˙103 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-12-01   to  2021-11-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

This project sets forth cutting-edge challenges in the field of Mathematical Physics that will be solved within a common framework by making novel use of classical tools of Harmonic Analysis such as Oscillatory Integrals and Trigonometric Sums, the Cauchy operator, and the so-called Carleman estimates. Three aspects will be covered: 1.Vortex Filament Equation (VFE) 2.Relativistic and Non-relativistic Critical Electromagnetic Hamiltonians 3.Uncertainty Principles (UPs) and Applications The interaction of vortex filaments is considered a key issue in order to understand turbulence which is seen by many as the most relevant unsolved problem of classical physics. VFE first appeared as an approximation of the dynamics of isolated vortex filaments. I want to understand what happens when at time zero the filament is a regular polygon. Preliminary theoretical arguments together with some numerical experiments suggest that the different corners behave like different vortex filaments that interact with each other in such a way that the dynamics seem chaotic. I will prove the so-called Frisch-Parisi conjecture, showing that behind this chaotic behavior there is an underlying algebraic structure that controls the dynamics. The Dirac equation, despite being one of the basic equations of Mathematical Physics, is very poorly understood from an analytical point of view. I will use the classical Cauchy operator in a modern way to explain some key Hamiltonian systems such as the MIT bag model for quark confinement. UPs are at the heart of different fields like Quantum Mechanics, Harmonic Analysis, and Information Theory. We want to use a new approach to analyze modern versions of UPs that are not well understood. In order to do this, I will look at the problem from the point of view of partial differential equations making novel use of the Carleman estimates. This analysis will also be extended to the discrete setting where even classical UPs such the one by Hardy are not solved yet


year authors and title journal last update
List of publications.
2018 Ignat L.; Stan D.
Asymptotic behaviour for fractional diffusion-convection equations
published pages: , ISSN: , DOI:
2016 L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions
published pages: 667-678, ISSN: 0010-3616, DOI: 10.1007/s00220-015-2500-z
Communications in Mathematical Physics 346/2 2020-01-24
2018 Thomas Ourmières-Bonafos, Konstantin Pankrashkin, Fabio Pizzichillo
Spectral asymptotics for δ -interactions on sharp cones
published pages: 566-589, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2017.09.026
Journal of Mathematical Analysis and Applications 458/1 2020-01-24
2017 Cassano B.; Fanelli L.
Gaussian Decay of Harmonic Oscillators and related models
published pages: , ISSN: , DOI:
2017 Junjie Zhang, Shenzhou Zheng
Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations
published pages: 1271-1289, ISSN: 1747-6933, DOI: 10.1080/17476933.2017.1357707
Complex Variables and Elliptic Equations 63/9 2020-01-24
2017 Ourmières-Bonafos T.; Vega L.
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
published pages: , ISSN: , DOI:
2015 Susana Gutiérrez, André de Laire
Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation
published pages: 1307-1350, ISSN: 0951-7715, DOI: 10.1088/0951-7715/28/5/1307
Nonlinearity 28/5 2020-01-24
2017 Susana Gutiérrez, André de Laire
The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions
published pages: , ISSN: , DOI:
2016 Naiara Arrizabalaga, Albert Mas, Luis Vega
An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
published pages: 483-505, ISSN: 0010-3616, DOI: 10.1007/s00220-015-2481-y
Communications in Mathematical Physics 344/2 2020-01-24
2018 Krejcirik, David; Laptev, Ari; Fanelli, Luca; Vega, Luis
On the improvement of the Hardy inequality due to singular magnetic fields
published pages: , ISSN: , DOI:
2018 Albert Mas, Fabio Pizzichillo
Klein’s paradox and the relativistic δ-shellinteraction in ℝ3
published pages: 705-744, ISSN: 2157-5045, DOI: 10.2140/apde.2018.11.705
Analysis & PDE 11/3 2020-01-24
2018 Cassano, Biagio; Pizzichillo, Fabio
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
published pages: , ISSN: 0377-9017, DOI: 10.1007/s11005-018-1093-9
Letters in Mathematical Physics 2020-01-24
2018 Beltran, David; Hickman, Jonathan; Sogge, Christopher D.
Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
published pages: , ISSN: , DOI:
2018 Valeria Banica, Luis Vega
Evolution of polygonal lines by the binormal flow
published pages: , ISSN: , DOI:
2017 Aingeru Fernández Bertolin, Luis Vega
Uniqueness properties for discrete equations and Carleman estimates
published pages: 4853-4869, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2017.03.006
Journal of Functional Analysis 272/11 2020-01-24
2018 Albert Mas
Characterization of balls as minimizers of an endpoint Gagliardo seminorm on the boundary
published pages: , ISSN: , DOI:
2018 B. Grébert, V. Vilaça Da Rocha
Stable and unstable time quasi periodic solutions for a system of coupled NLS equations
published pages: , ISSN: , DOI:
2017 N. Arrizabalaga, L. Le Treust, N. Raymond
On the MIT Bag Model in the Non-relativistic Limit
published pages: , ISSN: 0010-3616, DOI: 10.1007/s00220-017-2916-8
Communications in Mathematical Physics 2020-01-24
2018 Naiara Arrizabalaga, Loïc Le Treust, Nicolas Raymond
Extension operator for the MIT bag model
published pages: , ISSN: , DOI:
2017 Banica V.; Vega L.
Singularity formation for the 1-D cubic NLS and the Schrödinger map on $mathbb{S}^2$
published pages: , ISSN: 1534-0392, DOI: 10.3934/cpaa.2018064
Communications on Pure & Applied Analysis 2020-01-24
2018 Beltran, David; Cladek, Laura
Sparse bounds for pseudodifferential operators
published pages: , ISSN: , DOI:
2017 Mas A.; Pizzichillo F.
The relativistic spherical $delta$-shell interaction in $mathbb{R}^3$: spectrum and approximation
published pages: , ISSN: 0022-2488, DOI: 10.1063/1.5000381
Journal of Mathematical Physics 3 2020-01-24
20178 Cassano, Biagio
Sharp exponential localization for eigenfunctions of the Dirac Operator
published pages: , ISSN: , DOI:
2017 Pizzichillo F.
Singular Perturbation of the Dirac Hamiltonian
published pages: , ISSN: , DOI:
2018 Krejčiřík D.; Lotoreichik V.; Ourmières-Bonafos T.
Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers
published pages: , ISSN: , DOI:
2018 Luca Fanelli, David Krejčiřík, Luis Vega
Spectral stability of Schrödinger operators with subordinated complex potentials
published pages: 575-604, ISSN: 1664-0403, DOI: 10.4171/JST/208
Journal of Spectral Theory 8/2 2020-01-24
2016 Vladimir Lotoreichik, Thomas Ourmières-Bonafos
On the bound states of Schrödinger operators with δ-interactions on conical surfaces
published pages: 999-1028, ISSN: 0360-5302, DOI: 10.1080/03605302.2016.1168843
Communications in Partial Differential Equations 41/6 2020-01-24
2016 García A.; Vesalainen E.V.; Zubeldia M.
Discreteness of transmission eigenvalues for higher-order main terms and perturbations
published pages: , ISSN: 0036-1410, DOI: 10.1137/15M1053323
SIAM Journal on Mathematical Analysis 2020-01-24
2018 Luca Fanelli, David Krejcirik, Luis Vega
Absence of eigenvalues of two-dimensional magnetic Schroedinger operators
published pages: , ISSN: , DOI:
2018 David Beltran, João Pedro Ramos, Olli Saari
Regularity of fractional maximal functions through Fourier multipliers
published pages: , ISSN: , DOI:
2018 Yang Z-H.; Zheng S.
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
published pages: , ISSN: , DOI:
2018 Aingeru Fernández-Bertolin, Philippe Jaming
On unique continuation for solutions of the Schr{ö}dinger equation on trees
published pages: , ISSN: , DOI:
2018 Aingeru Fernandez-Bertolin, Karlheinz Gröchenig, Philippe Jaming
From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations
published pages: , ISSN: , DOI:
2018 Correia, Simão; Côte,Raphaël; Vega, Luis
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
published pages: , ISSN: , DOI:

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