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CC SIGNED

Combinatorial Construction

Total Cost €

0

EC-Contrib. €

0

Partnership

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Project "CC" data sheet

The following table provides information about the project.

Coordinator
THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD 

Organization address
address: WELLINGTON SQUARE UNIVERSITY OFFICES
city: OXFORD
postcode: OX1 2JD
website: www.ox.ac.uk

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 United Kingdom [UK]
 Total cost 1˙706˙729 €
 EC max contribution 1˙706˙729 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-01-01   to  2020-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD UK (OXFORD) coordinator 1˙706˙729.00

Map

 Project objective

Combinatorial Construction is a mathematical challenge with many applications. Examples include the construction of networks that are very sparse but highly connected, or codes that can correct many transmission errors with little overhead in communication costs. For a general class of combinatorial objects, and some desirable property, the fundamental question in Combinatorial Construction is to demonstrate the existence of an object with the property, preferably via an explicit algorithmic construction. Thus it is ubiquitous in Computer Science, including applications to expanders, sorting networks, distributed communication, data storage, codes, cryptography and derandomisation. In popular culture it appears as the unsolved `lottery problem' of determining the minimum number of tickets that guarantee a prize. In a recent preprint I prove the Existence Conjecture for combinatorial designs, via a new method of Randomised Algebraic Constructions; this result has already attracted considerable attention in the mathematical community. The significance is not only in the solution of a problem posed by Steiner in 1852, but also in the discovery of a powerful new method, that promises to have many further applications in Combinatorics, and more widely in Mathematics and Theoretical Computer Science. I am now poised to resolve many other problems of combinatorial construction.

 Publications

year authors and title journal last update
List of publications.
2018 Keevash, Peter
The existence of designs II
published pages: , ISSN: , DOI:
2019-04-18
2018 Keevash, Peter; Yepremyan, Liana
On the number of symbols that forces a transversal
published pages: , ISSN: , DOI:
2019-04-18
2018 Peter Keevash Eoin Long
Stability for vertex isoperimetry in the cube
published pages: , ISSN: , DOI:
2019-04-18
2017 Keevash, Peter; Yepremyan, Liana
Rainbow matchings in properly-coloured multigraphs
published pages: , ISSN: , DOI:
2019-04-18
2018 Peter Keevash, Eoin Long
A stability result for the cube edge isoperimetric inequality
published pages: 360-375, ISSN: 0097-3165, DOI: 10.1016/j.jcta.2017.11.005
Journal of Combinatorial Theory, Series A 155 2019-04-18
2016 PETER KEEVASH, EOIN LONG
On the Normalized Shannon Capacity of a Union
published pages: 766-767, ISSN: 0963-5483, DOI: 10.1017/S0963548316000055
Combinatorics, Probability and Computing 25/05 2019-04-18
2018 Matthew Jenssen Peter Keevash Will Perkins
\"Algorithms for #BIS-hard problems on expander graphs\"
published pages: , ISSN: , DOI:
2019-04-18
2018 Igor Balla, Felix Dräxler, Peter Keevash, Benny Sudakov
Equiangular lines and spherical codes in Euclidean space
published pages: 179-212, ISSN: 0020-9910, DOI: 10.1007/s00222-017-0746-0
Inventiones mathematicae 211/1 2019-04-18
2018 Coulson, Matthew; Keevash, Peter; Perarnau, Guillem; Yepremyan, Liana
Rainbow factors in hypergraphs
published pages: , ISSN: , DOI:
2019-04-18
2018 Keevash, Peter; Long, Eoin
Forbidden vector-valued intersections
published pages: , ISSN: , DOI:
2019-04-18

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