PhD defense "On hyperbolic 3-orbifolds of small volume."

A heuristic of Thurston says that volume is a good measure of the complexity of a hyperbolic 3-manifold. In this thesis, we present some results centered around this idea. We describe a joint work with J. DeBlois, H. A. Ekanayake, A. Gharagozlou, M. Fincher, and P. Mondal on constructing a census of complete, orientable, hyperbolic 3-orbifolds, commensurable with the figure eight knot complement, of volume at most 2v0, where v0 is the volume of a regular ideal tetrahedron in hyperbolic 3-space. We also classify the minimal volume complete, orientable, hyperbolic 3-orbifolds with one nonrigid cusp and one rigid cusp of type {6,3,2} or {4,4,2}.

Advisors: Jason DeBlois and Tom Hales

Committee Members: Neil Hoffman and Armin Schikorra