Speaker: Ilesanmi Adeboye,University of Michigan
Title of talk: Volumes of Hyperbolic Orbifolds.

Abstract: Various authors have previouslyestablished explicit lower bounds on the volume
of hyperbolic orbifolds of dimension three and of hyperbolic manifoldsof any dimension.
A hyperbolic n-orbifold is a quotient of hyperbolic $n$-space by adiscrete group
$\Gamma$ of isometries of $\mathbb{H}^{n}$.In pursuit of volume boundsfor hyperbolic
orbifolds, the presence of torsion elements in the group $\Gamma$ raisechallenges not
amenable to the techniques used in the manifold case. In this talk, wewill establish
lower bounds on the volume of hyperbolic orbifolds that depend ondimension and the
maximum order of the elliptic elements of $\Gamma$. We will alsodiscuss progress in
refining this result as well as applications.