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.

11 pages, 2 tables; minor changes, accepted in Groups Complexity Cryptology