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High Dimensional Expanders, Ramanujan Complexes and Codes

Total Cost €


EC-Contrib. €






Project "HIEXP" data sheet

The following table provides information about the project.


Organization address
postcode: 91904

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]
 Total cost 1˙592˙500 €
 EC max contribution 1˙592˙500 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-08-01   to  2021-07-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

'Expander graphs have been playing a fundamental role in many areas of computer science. During the last 15 years they have also found important and unexpected applications in pure mathematics. The goal of the current research is to develop systematically high-dimensional (HD) theory of expanders, i.e., simplicial complexes and hypergraphs which resemble in dimension d, the role of expander graphs for d = 1. There are several motivations for developing such a theory, some from pure mathematics and some from computer science. For example, Ramanujan complexes (the HD versions of the 'optimal' expanders, the Ramanujan graphs) have already been useful for extremal hypergraph theory. One of the main goals of this research is to use them to solve other problems, such as Gromov's problem: are there bounded degree simplicial complexes with the topological overlapping property ('topological expanders'). Other directions of HD expanders have applications in property testing, a very important subject in theoretical computer science. Moreover they can be a tool for the construction of locally testable codes, an important question of theoretical and practical importance in the theory of error correcting codes. In addition, the study of these simplicial complexes suggests new quantum error correcting codes (QECC). It is hoped that it will lead to such codes which are also low density parity check (LDPC). The huge success and impact of the theory of expander graphs suggests that the high dimensional theory will also bring additional unexpected applications beside those which can be foreseen as of now.'


year authors and title journal last update
List of publications.
2019 Eyal Lubetzky, Alex Lubotzky, Ori Parzanchevski
Random walks on Ramanujan complexes and digraphs
published pages: , ISSN: , DOI:
Journal of European Math. Soc. 2019-05-10
2018 Alexander Lubotzky, Zur Luria, Ron Rosenthal
On groups and simplicial complexes
published pages: 408-444, ISSN: 0195-6698, DOI: 10.1016/j.ejc.2018.01.009
European Journal of Combinatorics 70 2019-05-10
2018 David El-Chai Ben-Ezra, Alexander Lubotzky
The congruence subgroup problem for low rank free and free metabelian groups
published pages: 171-192, ISSN: 0021-8693, DOI: 10.1016/j.jalgebra.2017.01.001
Journal of Algebra 500 2019-05-10
2018 Marcus De Chiffre, Lev Glebsky, Alex Lubotzky, Andreas Thom
Stability, cohomology vanishing, and non-approximable groups
published pages: , ISSN: , DOI:
2018 Sylvain Cappell, Alexander Lubotzky, Shmuel Weinberger
A trichotomy theorem for transformation groups of locally symmetric manifolds and topological rigidity
published pages: 25-46, ISSN: 0001-8708, DOI: 10.1016/j.aim.2017.06.010
Advances in Mathematics 327 2019-05-10
2019 Nir Avni, Alexander Lubotzky, Chen Meiri
First order rigidity of non-uniform higher rank arithmetic groups
published pages: , ISSN: 0020-9910, DOI: 10.1007/s00222-019-00866-5
Inventiones mathematicae 2019-05-10
2019 Oren Becker, Alexander Lubotzky, Andreas Thom
Stability and Invariant Random Subgroups
published pages: , ISSN: , DOI:
Duke Journal of mathematics 2019-05-10
2018 Alexander Lubotzky, Zur Luria, Ron Rosenthal
Random Steiner systems and bounded degree coboundary expanders of every dimension
published pages: , ISSN: 0179-5376, DOI: 10.1007/s00454-018-9991-2
Discrete & Computational Geometry 2019-05-10

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The information about "HIEXP" are provided by the European Opendata Portal: CORDIS opendata.

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