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EXTPRO SIGNED

Quasi-Randomness in Extremal Combinatorics

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

EXTPRO project word cloud

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

spectacular additive researcher biology minimize active vs incorporated collection mathematical vibrant science truly ramsey obtain uses partitioned theoretical combinatorics started grant phenomenon hardest extremal techniques objects pi powerful extremely super computational graph deterministic ad variety em made asks attacking discipline celebrated random constrains ones caliber maximize arguments lemmas subareas randomness found attached discrete theory deep grown forefront quasi object isolated computer smaller regularity hypergraph tackling arithmetic hoc contributions group tools area certain fast roughly saturation tackled himself structure mature

Project "EXTPRO" data sheet

The following table provides information about the project.

Coordinator	TEL AVIV UNIVERSITY Organization address address: RAMAT AVIV city: TEL AVIV postcode: 69978 website: http://www.tau.ac.il/ 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	http://www.math.tau.ac.il/
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

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	TEL AVIV UNIVERSITY TEL AVIV UNIVERSITY Organization address address: RAMAT AVIV city: TEL AVIV postcode: 69978 website: http://www.tau.ac.il/ contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	IL (TEL AVIV)	coordinator	1˙221˙921.00

Map

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.

Publications

List of publications.
year	authors and title	journal	last update
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-FÃ¼redi 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
2016	KAAVE HOSSEINI, SHACHAR LOVETT, GUY MOSHKOVITZ, ASAF SHAPIRA 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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