A Spectral Gap Theorem in $SU(d)$

Understand

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3].

• The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU(2).