Thickness of skeletons of arithmetic hyperbolic orbifolds

We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger
and larger volumes give rise to triangulations of the underlying spaces whose
1-skeletons are harder and harder to embed nicely in Euclidean space.
To show this we generalize an inequality of Gromov and Guth to
hyperbolic orbifolds and find nearly optimal geodesic triangulations of
arithmetic hyperbolic n-orbifolds. This is a joint work with Hannah Alpert.