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Licensed Unlicensed Requires Authentication Published by De Gruyter April 20, 2018

Certifying numerical estimates of spectral gaps

Marek Kaluba ORCID logo EMAIL logo and Piotr W. Nowak ORCID logo


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.

MSC 2010: 16S34; 20C07; 20C40

Funding source: Narodowe Centrum Nauki

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

Award Identifier / Grant number: 677120-INDEX

Funding statement: 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).


We would like to thank Dawid Kielak and Taka Ozawa for valuable comments.


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Received: 2017-4-12
Published Online: 2018-4-20
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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