|
This is my webpage. I'm a mathematical physicist, leaning towards the pure end of the spectrum. This means that I study the mathematical structures that underlie my favourite physical theories. These days, that's mostly two-dimensional conformal field theories, especially the logarithmic ones, though I have dabbled in the past in integrability. On the mathematical side, I study the representation theory of vertex operator algebras and superalgebras. Sometimes I even prove theorems. But, pretty much anything that involves cool math is fine with me. One of my long-term interests is the class of conformal field theories known as the fractional-level Wess–Zumino–Witten models and the W-algebras obtained from them by quantum hamiltonian reduction. These are generally logarithmic, meaning that the corresponding vertex operator algebras have nonsemisimple module categories. This sounds hard (and it is), but there's a lot of cool 21st century mathematics tied up in this game, from “relaxed” versions of highest-weight modules to generalisations of modular tensor categories and exotic new types of modular forms. Physicists have also recently renewed their interest in this area because of newly found dualities connecting these types of conformal field theories to higher-dimensional supersymmetric gauge theories. I've said above that I'm a mathematical physicist and I stand by that declaration. However, I've also (sometimes for humorous effect) described myself as an experimental mathematician. In many ways, this is a better description because I'm mostly interested in understanding examples in detail. I'd like to think that the best parts of my work are in developing new tools, or new ways of looking at old tools, so that generalising from a few examples to an entire class becomes easy (and therefore boring). Luckily, there are always more examples throwing out more surprises, so I haven't gotten bored yet.
For my sins, I'm currently a Future Fellow of the Australian Research Council, which means I won't be doing a lot of teaching. However, I've not been taking it easy. Until recently, I was the Director of Postgraduate Teaching for the School of Mathematics and Statistics, the Chair of the Australian and New Zealand Association of Mathematical Physics and a member of both the Steering Committee and the Council of the Australian Mathematical Society. Luckily that's all stopped now, so if you want to talk math and/or math physics, please drop me a line! However, if you are inquiring about PhD scholarships, please read this first. By the way, guess who won the inaugural Rodney Baxter Prize in Mathematical Physics? |
 |
