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My current research is in the area of combinatorics, examining various lattice path problems. My current PhD work is centred on enumerating sets of paths on a diagonal lattice (either for a closed-form result or a generating function). This work is being supervised by Dr. Richard Brak and A.Prof. Aleks Owczarek, and I am partially funded by the ARC Centre of Excellence in the Mathematics and Statistics of Complex Systems.

Consider a set of walkers, with fixed starting and ending points, on a diagonal lattice. How many ways can they walk, provided they only take steps towards the right? If the walkers cannot visit the same place, they are vicious, and they are osculating if the paths can touch. I am currently trying to find the generating functions for these (and similar) problems, where the paths are weighted by the number of osculations.

My honours thesis (printed under a different name) was in Topology and Geometry, looking at combinatorial analogues to curvature (Riemannian and Ricci).


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Last Updated: 30/05/08
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