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PEPCo SIGNED

Problems in Extremal and Probabilistic Combinatorics

Total Cost €

0

EC-Contrib. €

0

Partnership

0

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0

 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.

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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 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 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 ErdoÌ‹s 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.

 Publications

year authors and title journal last update
List of publications.
2018 E. Aigner-Horev, D. Conlon, H. Hàn, 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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