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Opendata, web and dolomites

PEPCo SIGNED

Problems in Extremal and Probabilistic Combinatorics

Total Cost €

EC-Contrib. €

Partnership

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PEPCo project word cloud

Explore the words cloud of the PEPCo project. It provides you a very rough idea of what is the project "PEPCo" about.

least became triple subproblems so yield grown ergodic question finer discrete leads innocent questions tools structures sparse analogous mathematics closely theory fastest computer hyperedge seems random traced tura variety variant uncounted additional extremal maybe motivated al maximum ouml limited guiding imposing lemma pi quasirandom graphs extension et back goals pioneered area corresponding last dl interesting cardinality theoretical discipline solving asked fact line contributions hypergraphs szemer techniques prominent active regularity pseudorandom proposes gowers erdo assumptions unifying n combinatorics probabilistic deal hypergraph restrictions effort suggest missing hopefully despite ties framework manageable theme di eacute science mathematical fundamental central

Project "PEPCo" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITAET HAMBURG Organization address address: MITTELWEG 177 city: HAMBURG postcode: 20148 website: n.a. contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	Germany [DE]
Total cost	1˙800˙000 €
EC max contribution	1˙800˙000 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2016-COG
Funding Scheme	ERC-COG
Starting year	2017
Duration (year-month-day)	from 2017-10-01 to 2022-09-30

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITAET HAMBURG UNIVERSITAET HAMBURG Organization address address: MITTELWEG 177 city: HAMBURG postcode: 20148 website: n.a. contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	DE (HAMBURG)	coordinator	1˙800˙000.00

Map

Project 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 TuraÌn and it was established by ErdoÌ‹s 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 TuraÌn’s problem, maybe the most prominent open problem in the area. After solving an analogous question for graphs, TuraÌn 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 ErdoÌ‹s and SoÌs. 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.

Publications

List of publications.
year	authors and title	journal	last update
2018	E. Aigner-Horev, D. Conlon, H. HÃ n, Y. Person, M. Schacht Quasirandomness in hypergraphs published pages: , ISSN: 1077-8926, DOI:	Electronic Journal of Combinatorics	2019-08-06
2019	CHRISTIAN REIHER, MATHIAS SCHACHT FORCING QUASIRANDOMNESS WITH TRIANGLES published pages: , ISSN: 2050-5094, DOI: 10.1017/fms.2019.7	Forum of Mathematics, Sigma 7	2019-08-06

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