Presented by: Jessica Purcell, Monash University

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.

About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics. 

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

  • computer 
  • data projector
  • chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.


Richards Building (5)