Objective
The probabilistic method, pioneered by Paul Erds, can show the existence of combinatorial objects without hinting how to construct them effectively. Recent developments concerning the constructive version of Lovsz Local Lemma (LLL) showed how to modify the
probabilistic method to make it effective. This proposal lists four research directions in analysis, combinatorics, and cryptography, where this method opened new possibilities to go beyond our present knowledge.
1. The measurable version of LLL is the question whether the object, guaranteed by LLL, can additionally be measurable? In some special cases the answer is in the affirmative. What are the constraints which guarantee measurability, and when is it impossible to achieve this? Results are relevant for classical problems of measure group theory.
2. A novel approach improving the celebrated sunflower lemma also uses effective probabilistic tools. We will use a similar approach to improve the best estimates for multicolor Ramsey numbers, Schur numbers, and to explore a number of other classical problems.
3. Several new phenomena arise in extremal graphs when either the vertices or the edges are linearly ordered. To investigate them we use methods from effective probabilistic sampling. The answers would be relevant in discrete geometry, algorithm design, etc.
4. An emerging phenomenon in certain cryptographic primitives including secret sharing will be addressed: relaxing the strict requirements of correctness by allowing negligible errors can lead to significant improvement in efficiency. It is a direct consequence of the mostly unknown structure of the boundary of the entropy region. Using tools and results from the other parts of the project we will explore this boundary giving hints for why, and tools for where and when such efficiency gaps might occur.
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 computer and information sciences computer security cryptography
- agricultural sciences agriculture, forestry, and fisheries agriculture grains and oilseeds oilseeds
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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)
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-2021-ADG
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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.
1053 Budapest
Hungary
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.