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.
Forty years on
It is forty years on from the Dismissal, or coup, that ended the Whitlam government.
Riddle. Mystery. Enigma.
I appear in a rather excellent and fun episode of the ABC Radio National program Radiotonic.
Counting curves on surfaces, AustMS Sep 2015
On 30 September, 2015 I gave a talk at the Australian Mathematical Society Annual Meeting at Flinders University, in Adelaide. The talk was entitled “Counting curves on surfaces”. Slides from the talk are available.
Introduction to the AJ conjecture, Melbourne, August 2015
On 14 August 2015, I gave a talk in the Melbourne University Knot Invariant seminar, entitled “Introduction to the AJ conjecture”.
Why your calculator is a weapon
I gave a talk about the Defence Trade Cooperation Act, encryption, and number theory, as part of the Monash University LunchMaths seminar series, in August 2015. Slides are available.