Presented by: 
Jessica Purcell (Monash)
Mon 28 Aug, 2:00 pm - 3:00 pm

Alternating knots are some of the simplest knots to describe, and they occur frequently in low crossing knot tables. Most alternating knots have a complement that admits a hyperbolic metric: a metric with constant curvature -1. However, it is difficult to relate the hyperbolic geometry of these knots to their diagrams, and there are several open conjectures on possible relationships. Many of these conjectures are based on computer evidence. In this talk, we will address one such conjecture, concerning cusp volume. We will define the cusp volume, show examples, and discuss recent results showing that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot.