Explicit construction of Ramanujan bigraphs - Ballantine, Cristina; Maurischat, Kathrin (Women in Numbers Europe, 2015)
We construct explicitly an infinite family of Ramanujan graphs which are bipartite and biregular. Our construction starts with the Bruhat-Tits building of an inner form of SU_{3}(\mathbb{Q}_{p})SU3(Qp)SU_{3}(\mathbb{Q}_{p}). To make the graphs finite, we take successive quotients by infinitely many discrete co-compact subgroups of decreasing size.