Objective
Extremal and probabilistic combinatorics is a central and currently maybe the most active and fastest growing area in discrete mathematics. The field can be traced back to the work of Turán and it was established by Erdős through his fundamental contributions and his uncounted guiding questions. Since then it has grown into an important discipline with strong ties to other mathematical areas such as theoretical computer science, number theory, and ergodic theory.
The PI proposes a variety of extremal problems for hypergraphs and for sparse random and pseudorandom graphs. The work for hypergraphs is motivated by Turán’s problem, maybe the most prominent open problem in the area. After solving an analogous question for graphs, Turán asked to determine the maximum cardinality of a set E of three-element subsets of a given n-element set V such that for any 4 elements of V at least one triple is missing in E. This innocent looking problem seems to be out of reach by our current methods and despite a great deal of effort over the last 70 years, our knowledge is still very limited.
We suggest a variant of the problem by imposing additional restrictions on the distribution of the three-element subsets in E. These additional assumptions yield a finer control over the corresponding extremal problem. In fact, this leads to many interesting and hopefully more manageable subproblems, some of which were already considered by Erdős and Sós. We suggest a unifying framework for these problems and one of the main goals would be the development of new techniques for this type of problems. These additional assumptions on the hyperedge distribution are closely related to the theory of quasirandom discrete structures, which was pioneered by Szemerédi and became a central theme in the field. In fact, the hypergraph extension by Gowers and by Rödl et al. of the regularity lemma provide essential tools for this line of research.
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 arithmetics
- natural sciences computer and information sciences computational science
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- 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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H2020-EU.1.1. - EXCELLENT SCIENCE - 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.
ERC-COG - Consolidator Grant
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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-2016-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.
20148 Hamburg
Germany
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