On Thursday October 5 2017 I gave a talk in the Geometry and Topology seminar at the University of Sydney.
Tight contact structures on Seifert surface complements
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda’s method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number to be the leading coefficient of the Alexander polynomial. The Euler classes of the contact structures are identified with hypertrees in a certain hypergraph. Using earlier work, this establishes a connection between contact topology and the Homfly polynomial. We also show that the contact invariants of our tight contact structures form a basis for sutured Floer homology. Finally, we relate our methods and results to Kauffman’s formal knot theory.
The Tutte polynomial and knot theory, Monash Sep 2017
On September 25, 2017 I gave a talk as part of the Bill Tutte centenary celebration at Monash University.
Sciencey: Why do earphones get tangled?
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?
Tutte meets Homfly
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.
Polytopes, dualities, and Floer homology
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.
Adani: icon of Australian climate infamy
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.
An Off-the-Record Genocide: Global Resource Extraction Economy Provides Incentives to Destroy DR Congo Indigenous Groups
By Deborah S. Rogers of Initiative for Equality (IfE).
The work of Maryam Mirzakhani
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.
Maths week talk at PLC
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.