Research

August 11th, 2011

Relatively static information about my research interests will be on this page and its subpages.

My background is centred around mathematics. My PhD thesis was in abstract algebra (specifically noncommutative ring theory, more specifically structure of enveloping algebras of Lie superalgebras), but since 1999 I have worked primarily on combinatorics (especially generating functions).

I aim for a nice blend of combinatorics, discrete probability, algorithms, asymptotic analysis and symbolic computation. I see myself more as a theorizer than a problem-solver, although perhaps the picture is not as extreme as painted by Gian-Carlo Rota. I strongly believe in trying to find general, algorithmic solutions to problems, and implementing them when possible. This of course leads to an interaction with various areas of computer science. For example, I  did some work on broadcasting in communication networks, and am currently interested in questions in computational social choice theory related to multiagent systems in artifical intelligence.

My main areas of effort recently have been the study of asymptotics of generating functions (the AMS project) and in social choice theory, more specifically using combinatorial and probabilistic methods. Analysis of algorithms in the style of Donald Knuth is a heavy user of generating function techniques, so I have been led into that area, and want to explore it in more detail, including the experimental analysis aspects.

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