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
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- engineering and technology nanotechnology nano-materials two-dimensional nanostructures graphene
- natural sciences physical sciences quantum physics
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences physical sciences theoretical physics particle physics quarks
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-ADG - Advanced Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2014-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
48940 Leioa
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.