Project description
Finding solutions for geometric variational problems
Geometric variational problems are one of the oldest topics studied in mathematics. Their extremisers can describe equilibrium configurations of physical systems or provide preferred representatives of geometric shapes. Singularities of solutions of geometric variational problems can represent concentration of energies, fracture of materials or topological obstructions. The ERC-funded RISE project will use a variety of techniques to expand our understanding of geometric variational problems. In the process, it will solve key questions regarding the structure and regularity of singularities of their solutions providing new insights on old topics.
Objective
Solutions of geometric variational problems describe equilibrium configurations of physical systems or provide preferred representatives in homology and homotopy classes. Their singularities can be linked to concentration of energy or to topological obstructions, and their study is then of fundamental importance in their applications to Geometry and Physics.
This project intends to leverage on a series of novel techniques introduced by the PI in recent years to significantly improve our knowledge of geometric variational problems. The project will address a series of fundamental questions concerning the regularity and the structure of singularities of solutions to geometric variational problems whose answer will enhance our understanding of their behavior. This will be done according to three deeply interrelated lines of research: Regularity of minimizers and critical points in geometric measure theory, Singular structure of PDE constrained measures, Structure of free boundaries and of solutions to spectral optimization problems.
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.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2024-COG
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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.
35122 PADOVA
Italy
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.