Obiettivo 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 ApplicationsThe 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 Campo scientifico engineering and technologynanotechnologynano-materialstwo-dimensional nanostructuresgraphenenatural sciencesphysical sciencesquantum physicsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencestheoretical physicsparticle physicsquarksnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-ADG-2014 - ERC Advanced Grant Invito a presentare proposte ERC-2014-ADG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-ADG - Advanced Grant Istituzione ospitante UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA Contribution nette de l'UE € 903 352,60 Indirizzo BARRIO SARRIENA S N 48940 Leioa Spagna Mostra sulla mappa Regione Noreste País Vasco Bizkaia Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 672 103,00 Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA Spagna Contribution nette de l'UE € 903 352,60 Indirizzo BARRIO SARRIENA S N 48940 Leioa Mostra sulla mappa Regione Noreste País Vasco Bizkaia Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 672 103,00 Terza parte Soggetto giuridico diverso da un subappaltatore che è affiliato o legalmente collegato a un partecipante. Il soggetto svolge le attività secondo le condizioni stabilite nell’accordo di sovvenzione, fornisce beni o servizi per l’azione, ma non ha sottoscritto l’accordo di sovvenzione. Una terza parte rispetta le regole applicabili al suo partecipante correlato ai sensi dell’accordo di sovvenzione per quanto riguarda l’ammissibilità dei costi e il controllo delle spese. BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS Spagna Contribution nette de l'UE € 768 750,40 Indirizzo AL MAZARREDO 14 48009 Bilbao Mostra sulla mappa Regione Noreste País Vasco Bizkaia Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 768 750,40