Of all the things, what does Australian electoral politics concerns itself with?
Elections — or, how not to gnaw your arm off
Electoral politics in Australia. The mere thought of it makes me want to gnaw my arm off.
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”
Talk on trinities, hypergraphs, contact structures, March 2016
On 14 March, 2016 I gave a talk at Monash University in the Discrete Mathematics seminar. The talk was entitled “Trinities, hypergraphs, and contact structures”. Slides from the talk are available.
Love, the Answer to the Problem of Human Existence
A paean to, and exposition of, love, extracted as an extended set of quotations from Erich Fromm’s The Art of Loving.
More excrement
Poem about the material economy.
Trinities, SFH, contact structures, Kioloa Jan 2016
On 14 March, 2016 I gave a talk at Monash University in the Discrete Mathematics seminar. The talk was entitled “Trinities, hypergraphs, and contact structures”. Slides from the talk are available.
Counting curves on surfaces
Joint with Norman Do and Musashi Koyama.
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface S, and fix a number of points F on its boundary. We ask: how many configurations of disjoint arcs are there on S whose boundary is F?
We find that this enumerative problem, counting curves on surfaces, has a rich structure. For instance, we show that the curve counts obey an effective recursion, in the general framework of topological recursion. Moreover, they exhibit quasi-polynomial behaviour.
This “elementary curve-counting” is in fact related to a more advanced notion of “curve-counting” from algebraic geometry or symplectic geometry. The asymptotics of this enumerative problem are closely related to the asymptotics of volumes of moduli spaces of curves, and the quasi-polynomials governing the enumerative problem encode intersection numbers on moduli spaces. Furthermore, among several other results, we show that generating functions and differential forms for these curve counts exhibit structure that is reminiscent of the mathematical physics of free energies, partition functions, topological recursion, and quantum curves.
Force and restraint
Simone Weil wrote about the Iliad, how it dealt so beautifully with notions of force.