On September 25, 2017 I gave a talk as part of the Bill Tutte centenary celebration at Monash University.
An appearance in Sciencey, a new series from ABC that delivers quick, illuminating answers to some of the strangest questions in the universe. Why do earphones always tangle, and what does this tells us about the universe?
I’ll tell you about some extremely clever methods to tell graphs and knots apart, involving polynomials: the Tutte and HOMFLY polynomials. And they’re closely related.
This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.
Here we are, in the year 2017. With now 25 years of climate-change international agreements behind us, here we are still trying to build oil pipelines and coal mines.
In August 2017 I gave a talk on some of the mathematics of Maryam Mirzakhani, the great Iranian mathematician, first female Fields Medallist. This was a Monash LunchMaths seminar.
I gave an outreach talk to secondary students at PLC about mathematics and mathematicians, talking about, among other things, topology, Maryam Mirzakhani, and billiards, in July 2017. Slides are available.