Objective
Curvature is a fundamental concept in mathematics and physics, capturing how surfaces bend and how space is shaped. From Einstein’s theory of relativity to the behavior of biological membranes, curvature models have led to key advances in both theoretical and applied sciences. In recent years, there has been growing interest in nonlocal models, as they provide a more accurate description of real-world phenomena involving long-range interactions. A major challenge in this area is to define a rigorous notion of nonlocal curvature. This has been achieved for the Euclidean mean curvature, opening a rapidly developing field, but many central questions remain open for more complex curvatures and manifolds.
My goal is to advance this active line of research by studying nonlocal curvatures and their deep connections to conformal geometry. The project has two main components: first, I will introduce and analyze new nonlocal analogues of nonlinear curvature equations, focusing on the k-Hessian equations that arise in many geometric problems. Second, in the context of conformal geometry, I will extend the notion of Euclidean nonlocal mean curvature to abstract hypersurfaces and apply it as a boundary condition for the fractional Yamabe problem on manifolds. This will bring together two different communities: analysis and GMT experts studying nonlocal mean curvature on Euclidean surfaces, and geometric analysts working on conformal geometry on abstract manifolds. I will approach these objectives by integrating tools from nonlinear analysis, geometric PDEs, and nonlocal operators in a novel way.
The project will be hosted at the Universidad Autónoma de Madrid under the supervision of María del Mar González, a leading expert in the field, providing excellent opportunities for advanced training and strongly supporting my career development towards becoming an independent researcher.
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.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2025-PF
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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.
28049 Madrid
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.