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Quasi-Randomness in Extremal Combinatorics

Total Cost €


EC-Contrib. €






Project "EXTPRO" data sheet

The following table provides information about the project.


Organization address
address: RAMAT AVIV
city: TEL AVIV
postcode: 69978

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 Israel [IL]
 Project website
 Total cost 1˙221˙921 €
 EC max contribution 1˙221˙921 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-03-01   to  2021-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TEL AVIV UNIVERSITY IL (TEL AVIV) coordinator 1˙221˙921.00


 Project objective

Combinatorics is an extremely fast growing mathematical discipline. While it started as a collection of isolated problems that were tackled using ad-hoc arguments it has since grown into a mature discipline which both incorporated into it deep tools from other mathematical areas, and has also found applications in other mathematical areas such as Additive Number Theory, Theoretical Computer Science, Computational Biology and Information Theory.

The PI will work on a variety of problems in Extremal Combinatorics which is one of the most active subareas within Combinatorics with spectacular recent developments. A typical problem in this area asks to minimize (or maximize) a certain parameter attached to a discrete structure given several other constrains. One of the most powerful tools used in attacking problems in this area uses the so called Structure vs Randomness phenomenon. This roughly means that any {em deterministic} object can be partitioned into smaller quasi-random objects, that is, objects that have properties we expect to find in truly random ones. The PI has already made significant contributions in this area and our goal in this proposal is to obtain further results of this caliber by tackling some of the hardest open problems at the forefront of current research. Some of these problems are related to the celebrated Hypergraph and Arithmetic Regularity Lemmas, to Super-saturation problems in Additive Combinatorics and Graph Theory, to problems in Ramsey Theory, as well as to applications of Extremal Combinatorics to problems in Theoretical Computer Science. Another major goal of this proposal is to develop new approaches and techniques for tackling problems in Extremal Combinatorics.

The support by means of a 5-year research grant will enable the PI to further establish himself as a leading researcher in Extremal Combinatorics and to build a vibrant research group in Extremal Combinatorics.


year authors and title journal last update
List of publications.
2017 Dan Hefetz, Mykhaylo Tyomkyn
On the inducibility of cycles
published pages: 593-599, ISSN: 1571-0653, DOI: 10.1016/j.endm.2017.07.012
Electronic Notes in Discrete Mathematics 61 2019-10-10
2019 Guy Moshkovitz, Asaf Shapira
A sparse regular approximation lemma
published pages: 6779-6814, ISSN: 0002-9947, DOI: 10.1090/tran/7414
Transactions of the American Mathematical Society 371/10 2019-10-10
2019 Lior Gishboliner, Asaf Shapira
Efficient Removal Without Efficient Regularity
published pages: 639-658, ISSN: 0209-9683, DOI: 10.1007/s00493-018-3899-6
Combinatorica 39/3 2019-10-10
2019 Jacob Fox, Lior Gishboliner, Asaf Shapira, Raphael Yuster
The removal lemma for tournaments
published pages: 110-134, ISSN: 0095-8956, DOI: 10.1016/j.jctb.2018.10.001
Journal of Combinatorial Theory, Series B 136 2019-10-10
2017 Mykhaylo Tyomkyn
Lagrangians of hypergraphs: The Frankl-Füredi conjecture holds almost everywhere
published pages: 584-600, ISSN: 0024-6107, DOI: 10.1112/jlms.12082
Journal of the London Mathematical Society 96/3 2019-10-10
An improved lower bound for arithmetic regularity
published pages: 193-197, ISSN: 0305-0041, DOI: 10.1017/S030500411600013X
Mathematical Proceedings of the Cambridge Philosophical Society 161/02 2019-05-28
2016 Asaf Shapira, Raphael Yuster
Unavoidable tournaments
published pages: 191-207, ISSN: 0095-8956, DOI: 10.1016/j.jctb.2015.07.005
Journal of Combinatorial Theory, Series B 116 2019-05-28
2017 Reut Levi, Guy Moshkovitz, Dana Ron, Ronitt Rubinfeld, Asaf Shapira
Constructing near spanning trees with few local inspections
published pages: 183-200, ISSN: 1042-9832, DOI: 10.1002/rsa.20652
Random Structures & Algorithms 50/2 2019-05-28
2018 Guy Moshkovitz, Asaf Shapira
Decomposing a graph into expanding subgraphs
published pages: , ISSN: 1042-9832, DOI: 10.1002/rsa.20727
Random Structures & Algorithms 2019-05-28
2017 Asaf Shapira, Raphael Yuster
A tournament approach to pattern avoiding matrices
published pages: 477-505, ISSN: 0021-2172, DOI: 10.1007/s11856-017-1455-5
Israel Journal of Mathematics 217/1 2019-05-28

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