Details on the significance of the paper, overtwisted discs, characteristic foliations, and contact structures.
- pdf (14 pages)
Notes on Eliashberg’s 1989 paper, “Classification of overtwisted contact structures on 3-manifolds”
My attempt to flesh out a few of the details.
- pdf (7 pages)
Basic ideas about laminations
Based on Casson and Bleiler’s book.
- pdf (29 pages)
Hyperbolic structures with prescribed holonomy, Melbourne Jan 2006
In January 2006 I gave a talk on my masters work at the conference “Manifolds at Melbourne”.
- Here are the slides from the talk.
Masters thesis
In September 2005 I completed my masters at Melbourne, also under Craig Hodgson, entitled “From Algebra to Geometry: A Hyperbolic Odyssey”. I studied representations of surface groups and the existence of hyperbolic cone manifold structures with prescribed holonomy.
A pdf copy is available here (1.8 MB pdf, 171 pages).
Quadratic geography, algebraic extreme sports and magical Farey trees
Published in the Australian Mathematical Society Gazette “Mathellaneous” column.
Quadratic geography, algebraic extreme sports and magical Farey trees, Australian Mathematical Society Gazette, Vol. 31 No. 3.
- pdf (10 pages)
Games with Galois
In 2004 for the Mathellaneous column of the AustMS Gazette, I wrote an article about games and Galois theory. Lots of fun for all!
Published as Games with Galois, Australian Mathematical Society Gazette, Vol. 31 No. 2.
- pdf (10 pages)
I also slightly expanded this for Vinculum, a journal of the Mathematical Association of Victoria, on 30/7/07.
- pdf (14 pages)
A Beautiful Sequence
In 2004, I wrote a recreational article for the Australian Mathematical Society Gazette about one of my favourite sequences.
Published as A Beautiful Sequence, Australian Mathematical Society Gazette, Vol. 31 No. 1.
- pdf (6 pages)
The Exotic Realm of p-adic Numbers
Honours thesis
At the University of Melbourne I completed an honours thesis under Craig Hodgson, studying A-polynomials, representation varieties of 3-manifolds and their relationship with hyperbolic geometry.
A pdf copy is available here (0.8 MB, 122 pages).