Project description
Bridging geometry and analysis through harmonic function
The study of harmonic functions is a cornerstone of partial differential equations. Supported by the Marie Skłodowska-Curie Actions programme, the BP-HM-UC-AMC project aims to address the challenge of understanding boundary behaviour, which is critical for solving complex mathematical and physical problems. The project will investigate three linked areas: the stability of harmonic measures, unique continuation in ‘rough’ domains, and the regularity of area-minimising currents. By utilising techniques such as multiscale oscillation and the propagation of smallness, BP-HM-UC-AMC will bridge these diverse mathematical threads. Its goal is to achieve significant advances in analysis and geometry. By solving long-standing conjectures, this research may open new directions for future research, impacting how we understand the complex intersection of geometry and analysis.
Objective
The study of harmonic functions is a cornerstone of partial differential equations. This project pursues three connected threads related to boundary behaviour: (i) harmonic measure, where we study its dimension and quantitative stability; (ii) boundary unique continuation for harmonic functions, extending Bers’ theorem in the plane to elliptic operators and improving unique continuation results for Neumann problems in rough domains; and (iii) boundary regularity for area-minimizing currents, in both the real-analytic setting (towards White’s conjecture) and the smooth case. These threads are closely connected through multiscale oscillation and propagation of smallness phenomena, and progress on them would mark significant advances and open new directions in analysis, geometry, and PDE.
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 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.
08193 Cerdanyola Del Valles
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.