Objective
The packing problem associated with a family of sets F seeks a large subfamily of pairwise disjoint members of F. When F comprises the unit balls in d-space, this is the sphere packing problem, which for d = 3 was solved by Hales-Ferguson (Keplers conjecture). The cases d = 8, 24 have won Viazovska her Fields Medal. Much of discrete mathematics deals with dense packing problems. The asymptotic rate vs. distance problem, may be the most fundamental open problem about error correcting codes. It seeks the densest Hamming-sphere packing in discrete cubes. A linear code is a linear subspace of F_2n. Such codes are important both in theory and in practice. Here, we seek to maximize dim(C), when every nonzero vector in C has Hamming weight n. Despite its mathematical significance and practical importance, the answer remains unknown for all 1/2 > > 0, and our best upper bounds on the rate date from the 70s. Neither do we know if linear codes can be asymptotically as good as general codes. We have made some progress on these key questions of our proposal. The infinite d-regular tree Td is another important metric space where we seek dense sphere packing. It is easy to perfectly pack balls in Td, but not in a periodic manner. Periodic perfect sphere packings in Td coincide with Moore graphs - finite regular graphs of least diameter and largest possible girth (i.e. with no short cycles). Moore graphs were fully characterized in the 70s, yet we still cannot show that for fixed d 3 and large r, any periodic packing of r-spheres in Td must have vanishing density. Many important mathematicians, including Erds, Margulis, and Lubotzky-Phillips-Sarnak sought the largest possible girth of a d-regular n-vertex graph (d fixed, n ). We show how better upper bounds on linear codes yield progress here, whereas bounds on general codes would not do.We use computers as exploratory tools, e.g. to test our new bounds on codes, yet we publish only humanly verifiable proofs.
Fields of science (EuroSciVoc)
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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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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)
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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
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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-2023-ADG
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91904 Jerusalem
Israel
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