I'm originally from Perth, a graduate of Rossmoyne Senior High School. I did my BSc at Murdoch University, burdening myself with a double degree in mathematics and physics (and 3/4 of a degree in chemistry). My honours research involved operator theory and three-body quantum scattering. I then moved to the University of Western Australia where I obtained a masters degree in the theory of topological chaotic dynamics and its application to noise reduction algorithms.
I then moved to Adelaide to start a PhD at the University of Adelaide. There I was introduced to the wonderful world of conformal field theory, and tried in vain to pick up the rudiments of string theory. With a little Lie theory, algebraic topology, differential geometry, and commutative algebra, I wrote a thesis on D-brane charges and fusion rings in Wess-Zumino-Witten models. The last two years of my doctoral studies were completed as a guest in the maths department of La Trobe University in Melbourne.
My first postdoc was in Québec with Pierre Mathieu. There, I worked on extending the chiral algebras of various conformal field theories, learned how to make a fool of myself in french and made some forays into the world of logarithmic conformal field theory. This was followed by an EU fellowship with the DESY Theory Group in Hamburg with Jörg Teschner. I continued to play with logarithmic conformal fields, and learned a little about deformed conformal field theories, integrable models and quantum groups. The highlight of my time in Europe was definitely the cheese.
Returning to Canada, I spent a year in the wonderfully cosmopolitan city of Montréal, working with Yvan Saint-Aubin in the Centre de Recherches Mathématiques. We worked together on aspects of Temperley-Lieb algebras as they apply to logarithmic conformal field theory. I also did some lecturing for McGill University. At the moment, the ARC has kindly supported my desire to come back home. I'm now an Australian Research Fellow at the ANU. Five years should give me enough time to determine if one can find good cheese in this country. Wish me luck! I promise to return the favour someday...
I'm interested in conformal field theory, specifically in the mathematical aspects of its algebraic formulation. This means that much of what I do could be classed as representation theory. Currently, I'm studying examples of conformal field theories in which the correlation functions exhibit logarithmic singularities. In representation-theoretic terms, these logarithmic theories are built from representations which are indecomposable but not irreducible. Such theories arise naturally when considering so-called non-local observables (crossing probabilities, fractal dimensions) in the conformal limit of many exactly solvable lattice models (percolation, Ising). They are also relevant to string-theoretic considerations, especially when the target space admits non-compact or fermionic directions, AdS/CFT, and perhaps even to black hole holography. In mathematics, there is a tantalising suggestion that logarithmic conformal field theory and Schramm-Loewner Evolution may be equivalent in some sense.
My research aims to further knowledge of the algebraic structures underpinning logarithmic conformal field theories. Expected outcomes include an improved understanding of the applications to statistical physics and string theory, as well as developing further beautiful connections with pure mathematics.