Seminar

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

I will give some details of a successful search, joint with Arshia Gharagozlou and Neil Hoffman, for knot complements in $S^3$ with two properties — (1) they admit complete hyperbolic structures containing closed, embedded totally geodesic surfaces, and (2) they have hidden symmetries — among covering spaces of the rich class of “prism orbifolds”. Key search phases were pre-filtering: ruling out the prism orbifolds that wouldn’t yield knot complement covers; enumeration; filtering out covers lacking necessary conditions to be knot complements; and recognizing knot complements. I’ll describe the computational tools we used and the theoretical results undergirding them.