Q: What led you into science and your chosen area of research?
A: At school, I was interested (among other things) in the natural sciences and in mathematics. I then thought physics would be a subject where I could be involved with both. As a student, I became increasingly interested in mathematics and the more conceptual aspects of physics, and this led me to concentrate on the theory of elementary particles and later on mathematical physics.
A: In this paper, I derive some exact results about a system of vortices in a field theory with gauge symmetry U(1) (i.e. the circle). Vortices are examples of "solitons" (extended particles) in two dimensions, and a lot of details about their physical behaviour at low energy can be understood by studying the geometry of the space of all vortex configurations with the same vortex number. What I did in the paper was to extend a well-known model for vortex dynamics to incorporate interactions between the vortices and an external potential in a natural way. For a simple potential (namely the height function on a sphere where the vortices live), I realised that you can get just enough information from rotational symmetry to compute the partition function of the system exactly and derive some thermodynamical consequences from it. My calculations make use of a famous localisation formula in symplectic geometry, and provide insight on the vortex system independent of the particular potential I have used. I should point out that partition functions for this system had been calculated before (using other methods), but only in a noninteracting regime where the vortices exert no net forces among themselves. My work is original as it is a first step to understand the fully interacting regime of vortices on a sphere; besides, it is very satisfactory that all my results are analytical.
Q: What research projects are you working on at the moment?
A: Most of the projects I am involved with at the moment are connected to the physics of topological solitons -- not only vortices but also monopoles and solitons in sigma-models. For example, a project that I am just completing (with Paul Norbury at the University of Melbourne) addresses the calculation of the mass of magnetic monopoles living in hyperbolic 3-space when you are given their "spectral curve" (a compact Riemann surface associated with them). These objects have a rich structure that has been much exploited in the euclidean limit, but then the geometry simplifies and monopoles of different masses can be identified. We managed to compute several explicit examples of spectral curves of any mass, and now hope to understand better how changing the mass qualitatively affects the way we can think about hyperbolic monopoles.
Q: What do you think will be the next big breakthrough in your field?
A: This is a difficult question, as no one can predict where a ground-breaking idea might come from. On the broader stage of high-energy physics, however, I expect that the next firm long step forward might well be the vindication (or not) of the ideas surrounding supersymmetry, which will be probed experimentally at the LHC accelerator, scheduled to start running in 2007. These ideas have been useful in mathematics and it is almost unbelievable that nature would not make use of them too.
Q: What book are you reading right now?
A: I usually read several books at the same time, picking one or another at a given moment according to mood. My current list is: (i) Looking for Spinoza by Antonio Damasio; (ii) Der Blaue Reiter by Wassily Kandinsky and Franz Marc (manifesto of the expressionistic movement based in Munich, pre-WWI); (iii) Eucalyptus by Murray Bail (I got interested in Australian fiction recently); (iv) the second book of short stories by Antonio Lobo Antunes; (v) Bird Life by Ian Rowley, an account of the birdlife of Australia.
Q: If you could have dinner with any 3 people, past or present,
who would they be and why?
A: This is another difficult one. Although I have no complaints about the living people I've had dinner with recently, I would definitely choose "past" illustrious guests if I were given the choice. Someone like Dirac wouldn't do, as interaction at table is also important. I might choose (say) Einstein, Goethe and Feynman. Hard to say which language(s) would be spoken -- Feynman is known to have been fluent in Portuguese.
Q: What has been the most exciting moment in your career so far?
A: There have been exciting moments, but I hope the most exciting one is still to come.