University of Chicago
Department of Mathematics

Jorgensen and Thurston demonstrated that the volumes of hyperbolic 3-manifolds are well-ordered. It is an outstanding problem to find the minimal volume hyperbolic 3-manifolds and orbifolds. The Weeks manifold, with volume =.9427... is conjectured to be the smallest volume hyperbolic 3-manifold. We'll discuss the status of this problem, as well as explain results on lower bounds of volumes of hyperbolic 3-manifolds and orbifolds with various restrictions on their topology. The beginning of the talk will include a brief introduction to hyperbolic orbifolds.