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 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.
I’m quite skeptical of the “positive psychology” movement, as it encourages the individualisation of some problems that are really social.
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.
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.
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.
On September 25, 2017 I gave a talk as part of the Bill Tutte centenary celebration at Monash University.