This letter was written by prominent academic experts and signed by over 500 scientists including myself.
Their profit, to decipher all this mess: the prehistory of AI mathematics and the new millennium
On the mathocalypse.
Geometry of Ptolemy equations for hyperbolic 3-manifolds, Monash, September 2026
On 9 September 2026 I gave a talk in the Monash Topology seminar. It was entitled “Geometry of Ptolemy equations for hyperbolic 3-manifolds”.
Curving in the hyperbolic plane
Here is some fun about the curvature of curves in the hyperbolic plane.
Leiden
We can add to the sordid list of uses of mathematics artificial intelligence automating surveillance and genocide.
Physical aspects of circle packings, ANZAMP, Feb 2026
On 11 February 2026 I gave a talk at the ANZAMP conference. It was entitled “Physical aspects of circle packings”.
Generalised Kauffman Clock Theorems
Kauffman’s clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact oriented surfaces.
Lightning talk on circle packing at Melbourne Uni
On 11 August 2025, I gave a lightning talk on circle packing at Melbourne Uni.
On Geometric Triangulations of Double Twist Knots
In this paper we construct two different explicit triangulations of the family of double twist knots K(p,q) using methods of triangulating Dehn fillings, with layered solid tori and their double covers. One construction yields the canonical triangulation, and one yields a triangulation that we conjecture is minimal. We prove that both are geometric, meaning they are built of positively oriented convex hyperbolic tetrahedra. We use the conjecturally minimal triangulation to present eight equations cutting out the A-polynomial of these knots.
Spinors and lambda lengths, NUS Singapore, December 2024
On 9 December 2024 I gave a talk in the NUS Topology, Geometry and Dynamics seminar. It was entitled “Spinors and lambda lengths”.