Certifying Numerical Estimates of Spectral Gaps

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 Kazhdan property (T). A software for such optimisation for other finitely presented groups is provided.

Publication
Groups Complexity Cryptology, Volume 10, Issue 1 (2018), p. 33-41

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Marek Kaluba
Assistant Professor

My research interests include computational algebra, geometric group theory (in particular: property (T)) and surgery aspects of manifolds.