Objective
In 2006 Cohn and Kumar have conjectured that the A2 lattice is universally optimal, meaning that it has the lowest potential energy among all configurations of the same density for all completely monotone potentials. This conjecture has several very important corollaries. Among other consequences, it is known that it implies a positive solution to the 2D crystallization problem, a major unsolved problem coming from materials science, and it also implies a conjecture on the emergence of the triangular lattice of Abrikosov vortices in the Landau-Ginzburg theory of superconductivity.
Recently, the 8 and 24-dimensional cases of the Cohn-Kumar conjecture have been positively resolved using novel interpolation formulas for radial Schwartz functions. This formula recovers a radial function from the data of it and its Fourier transform on a discrete set of radii, and its construction uses classical modular and quasi-modular forms.
In this project we will prove a significant generalization of these interpolation formulas with a view towards applications in extremal problems in Fourier analysis. To prove these formulas we will develop new analytic and numerical techniques for solving certain types of functional equations in one complex variable. Finally, based on these proposed interpolation formulas we will give a refinement of the Cohn-Kumar conjecture in dimension 2 and use it to attack the full conjecture in this case.
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.
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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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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-2022-STG
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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.
75794 PARIS
France
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.