Certifying numerical estimates of spectral gaps
Marek Kaluba, Piotr W. Nowak · journal of Groups complexity cryptology · 2018
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.