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High Dimensional Expanders, Ramanujan Complexes and Codes

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."
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Host institution

THE HEBREW UNIVERSITY OF JERUSALEM

Address

Edmond J Safra Campus Givat Ram
91904 Jerusalem

Israel

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 592 500

Beneficiaries (1)

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THE HEBREW UNIVERSITY OF JERUSALEM

Israel

EU Contribution

€ 1 592 500

Project information

Grant agreement ID: 692854

Status

Ongoing project

  • Start date

    1 August 2016

  • End date

    31 July 2021

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 1 592 500

  • EU contribution

    € 1 592 500

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel