Finite quotients of Bruhat-Tits buildings as geometric expanders

Understand

In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property.

• Their explicit constructions are finite quotients of $\tilde{A_d}$-buildings, for $d\geq 2$, over local fields.
• In this paper, this result is extended to general high rank Bruhat-Tits buildings.