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.

## Talk on Counting Curves on Surfaces, September 2018

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”.

## The algebra and geometry of contact categories, Melbourne July 2018

On Monday July 23 2018 I gave a talk in the Geometry and Topology seminar at the University of Melbourne.

## 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.

## 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.

## 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.

## Polytopes, dualities, and Floer homology

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.

## Morse structures on partial open books with extendable monodromy

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.

## AustMS talk, December 2016

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.