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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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CiteScore 2017: 0.32

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1869-6104
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Certifying numerical estimates of spectral gaps

Marek KalubaORCID iD: http://orcid.org/0000-0002-8777-8223 / Piotr W. NowakORCID iD: http://orcid.org/0000-0002-6519-004X
Published Online: 2018-04-20 | DOI: https://doi.org/10.1515/gcc-2018-0004

Abstract

We establish a lower bound on the spectral gap of the Laplace operator on special linear groups using conic optimisation. In particular, this provides a constructive (but computer assisted) proof that these groups have the Kazhdan property (T). Software for such optimisation for other finitely presented groups is provided.

Keywords: Property (T); Kazhdan constants; special linear group; semidefinite programming

MSC 2010: 16S34; 20C07; 20C40

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About the article

Received: 2017-04-12

Published Online: 2018-04-20

Published in Print: 2018-05-01


Funding Source: Narodowe Centrum Nauki

Award identifier / Grant number: 2015/19/B/ST1/01458

Funding Source: H2020 European Research Council

Award identifier / Grant number: 677120-INDEX

The first author has been partially supported by the National Science Centre, under grant number 2015/19/B/ST1/01458. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 677120-INDEX).


Citation Information: Groups Complexity Cryptology, Volume 10, Issue 1, Pages 33–41, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2018-0004.

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