It’s always nice, intellectually, when two apparently unrelated areas collide. I had an experience of this sort recently with an area of mathematics — one very familiar to me — and an ostensibly completely distinct area of science. On the
“The beauty of mathematics shows itself to patient followers” — The work of Maryam Mirzakhani
The recent passing of Maryam Mirzakhani came as a shock to many of us in the world of mathematics. Together with Norman Do, we attempt to share something about Mirzakhani’s work.
The disempowerment of positive thinking
I’m quite skeptical of the “positive psychology” movement, as it encourages the individualisation of some problems that are really social.
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.
Is the traditional mathematics blackboard lecture dead?
The Australian Mathematical Society Annual Meeting this year included a public debate on the topic “Is the traditional mathematics blackboard lecture dead?” I was on the affirmative team.
Some pure mathematics and consciousness
In November 2017 I gave a talk to the Monash Consciousness Research Laboratory (Tsuchiya Lab). I talked about some pure mathematical ideas that have appeared in the literature on the frontiers of neuroscience and the study of consciousness — gauge theory, and category theory.
What is to be done, and the Paradox of Choice
The real problem is not that we are overloaded with too many ideas about what to do. The real problem is that we do not have enough ideas about where we want to go.
Plane graphs, special alternating links, and contact geometry, Sydney Oct 2017
On Thursday October 5 2017 I gave a talk in the Geometry and Topology seminar at the University of Sydney.
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?