(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.
Lovely Liouville geometry
Limitless as that space too narrow for its inspirations
In which I recall, via neurologist Oliver Sacks, some musings of Sylvester from 1877 on the limitlessness of mathematics.
A-infinity algebras, strand algebras, and contact categories
In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered Floer theory. Being isomorphic to the homology of a differential graded algebra, this contact category algebra has an A-infinity structure. In this paper we investigate such A-infinity structures in detail. We give explicit constructions of such A-infinity structures, and establish some of their properties, including conditions for the nonvanishing of A-infinity operations. Along the way we develop several related notions, including a detailed consideration of tensor products of strand diagrams.
Knot Invariants and Cluster Algebras, AustMS Dec 2017
On 12 December 2017 I gave a talk in the Topology session of the 2017 meeting of the Australian Mathematical Society, entitled “Knot invariants and cluster algebras”.
Plane graphs and Grassmannian positivity, September 2017
On 20 September, 2017 I gave a talk in the Monash topology seminar. The talk was entitled “Plane graphs and Grassmannian positivity”.
Holy h-principle, Batman!
In which I attempt to explain some of the ideas behind the h-principle.
The Impact of Impact
On some aspects of the research funding system in the UK and Australia.
Talk on hyperbolic volume and Mahler measure, April 2016
On 8 April, 2016 I gave a talk at the University of Melbourne in the Knot Invariants seminar. The talk was entitled “Hyperbolic volume and the Mahler measure of the A-polynomial”
Geometric quantisation and A-polynomials, June 2015
On 12 June, 2015 I gave a talk at the University of Melbourne, in the Moduli Spaces seminar. The talk was entitled “Geometric quantisation and calculation of A-polynomials”.
The A-polynomial, symplectic geometry, and quantisation, May 2015
On 15 May, 2015 I gave a talk at the University of Melbourne, in the Moduli Spaces seminar. The talk was entitled “The A-polynomial, symplectic geometry, and quantisation”.