In September 2018 I gave a talk on the life and mathematics of Maryam Mirzakhani in the School of Physical and Mathematical Sciences colloquium at NTU in Singapore.
On 19 September 2018 I gave a talk at the National University of Singapore (NUS) in the Topology and Geometry seminar. The talk was entitled “Counting Curves on Surfaces”.
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.
On September 25, 2017 I gave a talk as part of the Bill Tutte centenary celebration at Monash University.
This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.
Joint with Joan Licata.
We extend the notion of Morse structure on an open book to extendable partial open books in order to study contact 3-manifolds with convex boundary.
On 6 December, 2016, I gave a talk at the Austrlaian Mathematical Society Annual Meeting at ANU, Canberra. The talk was entitled “Strand algebras and contact categories”. Slides from the talk are available.