I am interested in everything. In particular I am interested in mathematics. Most of my mathematical research has been in the broad field of geometry and topology. My fields of research include contact topology, symplectic topology, hyperbolic geometry, Heegaard Floer homology and topological quantum field theory.

Here you can find my research papers, talks, theses, and my translations of other papers.

###### Research papers and preprints

Follow the links for abstracts, publication details, and full text.

- A symplectic basis for 3-manifold triangulations
- A-polynomials, Ptolemy varieties and Dehn filling
- The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras
- A-infinity algebras, strand algebras, and contact categories
- Tight contact structures on Seifert surface complements
- Polytopes, dualities, and Floer homology
- Morse structures on partial open books with extendable monodromy
- Strand algebras and contact categories
- Counting curves on surfaces
- Strings, fermions and the topology of curves on annuli
- Topological recursion and a quantum curve for monotone Hurwitz numbers
- An explicit formula for the A-polynomial of twist knots
- Twisty itsy bitsy topological field theory
- Contact topology and holomorphic invariants via elementary combinatorics
- Dimensionally-reduced sutured Floer homology as a string homology
- Itsy bitsy topological field theory
- Sutured TQFT, torsion, and tori
- The hyperbolic meaning of the Milnor–Wood inequality
- Hyperbolic cone-manifold structures with prescribed holonomy II: higher genus
- Hyperbolic cone-manifold structures with prescribed holonomy I: punctured tori
- Sutured Floer Homology, Sutured TQFT and Non-Commutative QFT
- Chord diagrams, contact-topological quantum field theory, and contact categories
- Chord diagrams, topological quantum field theory, and the sutured Floer homology of solid tori

###### Research talks

Some talks have slides available.

- Tsinghua topology seminar: A symplectic approach to 3-manifold triangulations and hyperbolic structures
- Monash topology talk on Symplectic approach to 3-manifold Triangulations, September 2022
- Talk at Knots in Washington 49.75
- A Symplectic Basis for 3-manifold Triangulations, AustMS 2021
- Five-minute surrealist antiwar exposition of topological data analysis
- Ptolemy vs Thurston in Hyperbolic Geometry and Topology, AustMS 2020
- A-polynomials, Ptolemy varieties, and Dehn filling, Melbourne June 2020
- Monash topology talk on Circle packings, Lagrangian Grassmannians, and Scattering Diagrams, April 2020
- AustMS 2019 talk on geometry and physics of circle packings
- Talk in Monash discrete mathematics seminar, September 2019
- Monash topology talk on sensitivity conjecture and Clifford algebras, July 2019
- The beauty of mathematics shows itself to patient followers
- Talk on Counting Curves on Surfaces, September 2018
- The algebra and geometry of contact categories, Melbourne July 2018
- Some pure mathematics and consciousness
- Plane graphs, special alternating links, and contact geometry, Sydney Oct 2017
- The Tutte polynomial and knot theory, Monash Sep 2017
- AustMS talk, December 2016
- Talks at Low-dimensional topology workshop, Oct-Nov 2016
- Talk on hyperbolic volume and Mahler measure, April 2016
- Talk on trinities, hypergraphs, contact structures, March 2016
- Trinities, SFH, contact structures, Kioloa Jan 2016
- Counting curves on surfaces, AustMS Sep 2015
- Geometric quantisation and A-polynomials, June 2015
- The A-polynomial, symplectic geometry, and quantisation, May 2015
- Contact topology and holomorphic invariants, Tokyo Feb 2015
- Strings, fermions, curves on surfaces, ANZMC Dec 2014
- Strings, fermions, curves on surfaces, Unimelb Oct 2014
- Discrete contact geometry, May 2014
- A Yang-Baxter equation from sutured Floer homology, Sep 2013
- Sutures, quantum groups, TQFT, May 2013
- Contact topology and elementary combinatorics, April 2013
- Contact topology and holomorphic invariants via elementary combinatorics, Monash Dec 2012
- Field-theoretic ideas from contact geometry, ANZAMP 2012
- Itsy bitsy topological field theory, USC April 2012
- Itsy bitsy topological field theory, MIT April 2012
- Itsy bitsy topological field theory, Monash Mar 2012
- Hyperbolic cone-manifolds with prescribed holonomy, Maryland Nov 2011
- Sutured Floer homology and TQFT, Harvard May 2011
- Sutured topological quantum field theory, Brown April 2011
- Talks at Columbia University, Oct 2010
- Sutured TQFT and contact elements in SFH, Boston College Sep 2010
- Hyperbolic cone-manifolds with prescribed holonomy, Singapore Jul 2010
- SFH and contact TQFT, Jussieu May 2010
- SFH and contact TQFT, Lyon May 2010
- SFH and contact TQFT, ULB Brussels Apr 2010
- Sutured topological quantum field theory, Michigan Apr 2010
- Chord diagrams and contact TQFT, Uppsala Feb 2010
- Chord diagrams and contact-TQFT, Melbourne Jan 2010
- Chord diagrams, contact-TQFT and contact categories, Grenoble Dec 2009
- Chord diagrams, contact-TQFT and contact categories, Nantes Dec 2009
- Chord diagrams and SFH of solid tori, Columbia Apr 2009
- Chord diagrams, TQFT, and SFH of solid tori, Stanford Mar 2009
- Hyperbolic structures with prescribed holonomy, Melbourne Jan 2006

###### Theses

###### Translations

It’s plus facile for me to lire mathematics in English than in French.

- Translation of Giroux’s 1991 paper “Convexite en topologie de contact”
- Translation of Martinet’s 1971 paper “Formes de contact sur les varietes de dimension 3”

###### Notes

Here are a few notes I have written on various papers and books by other people; very sketchy, missing proofs, probably full of mistakes, but attempting to convey the gist of what’s going on. They are meant to be easier to read than the original, or as an adjunct. They are to be read for the gist, not the details. That said, if you want to point out mistakes or make suggestions, go ahead!

- Summarise your maths research in one slide, Dan
- Uniqueness of contact structures and tomography
- Convex surfaces and tomography
- Liouville structures and convex surfaces
- From Liouville geometry to contact geometry
- Lovely Liouville geometry
- Complex vector spaces, duals, and duels
- Notes on Giroux’s 1991 paper, “Convexite en topologie de contact”
- Notes on Eliashberg’s 1992 paper, “Contact 3-manifolds twenty years since J. Martinet’s work”
- Notes on Eliashberg’s 1989 paper, “Classification of overtwisted contact structures on 3-manifolds”
- Basic ideas about laminations