Highlights from "The Ramanujan Property for Simplicial Complexes"

This paper brings the main definitions and results from "The Ramanujan Property for Simplicial Complexes" [arXiv:1605.02664]. No proofs are given.
Given a simplicial complex X and a group G acting on X, we define Ramanujan quotients of X. For G and X suitably chosen this recovers Ramanujan k-regular graphs and Ramanujan complexes in the sense of Lubotzky, Samuels and Vishne. Deep results in automorphic representations are used to give new examples of Ramanujan quotients when X is the affine building of an inner form of GLn over a local field of positive characteristic.