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.
Knot Invariants and Cluster Algebras, AustMS Dec 2017
On 12 December 2017 I gave a talk in the Topology session of the 2017 meeting of the Australian Mathematical Society, entitled “Knot invariants and cluster algebras”.
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.
Tight contact structures on Seifert surface complements
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda’s method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number to be the leading coefficient of the Alexander polynomial. The Euler classes of the contact structures are identified with hypertrees in a certain hypergraph. Using earlier work, this establishes a connection between contact topology and the Homfly polynomial. We also show that the contact invariants of our tight contact structures form a basis for sutured Floer homology. Finally, we relate our methods and results to Kauffman’s formal knot theory.
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.
Plane graphs and Grassmannian positivity, September 2017
On 20 September, 2017 I gave a talk in the Monash topology seminar. The talk was entitled “Plane graphs and Grassmannian positivity”.