4 problems

A spherical building is a simplicial complex with the spherical building structure, and its coboundary expansion is the corresponding expansion parameter for cochains. Let $d$ be a…

Parzanchevski et al.'s conjecture. An inequality of the form

Let $k$ be a global field, ${\cal O}$ its ring of integers, $S$ a finite set of valuations of $k$ including all archimedean ones, and ${\cal O}_S$ the ring of $S$-integers. Let $G$…

Let $A_{n+1}({\mathbb F}_q)$ be the $n$-dimensional building associated with the projective geometry over the finite field ${\mathbb F}_q$, and let $h_{n-1}$ denote its normalized…