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Isaac Burke (B.Sc. Mathematics, 2012) is one of four NUI Galway students who were winners of the 2012 Undergraduate Awards - an international academic awards programme that identifies top students across the globe through their innovative undergraduate research.
Isaac's award was in the Mathematical & Physical Sciences category for his final year project, "Finding a non-broken circuit basis for the Orlik-Solomon algebra of an arrangement of hyperplanes", supervised by Dr Goetz Pfieffer. Other NUI Galway winners were Neasa O'Callaghan (Ancient & Classical Studies), Cathal Kelly (Engineering & Mechanical Sciences) and Marek Bohacek (Psychology).
Isaac's research was based on the following result published by Peter Orlik and Louis Solomon in 1980: "Let A, X be an arrangement of hyperplanes and the associated complement. Then the cohomology ring H(X) is isomorphic to the Orlik-Solomon Algebra O(A) of the hyperplane arrangement." Orlik and Solomon proved that a special "non-broken circuit" basis existed for O(A).However, the authors did not answer the question of how to find this basis given an arbitrary arrangement of hyperplanes. This question is comprehensively answered in the award-winning paper. The method of research involved investigating various hyperplane arrangements and examining the mathematical structure of the O(A) over those arrangements, seeking to find a pattern amongst the diversity. Along the way a corollary to an existing theorem was proved and several new definitions were formulated. The end result is a general algorithm which, for a specific hyperplane arrangement A, outputs a non-broken circuit basis for O(A).
Panels of international academics assessed the 2890 coursework entries that were received from students attending third level institutions across Ireland, the USA, UK and Canada, and selected two winners per academic category.
As part of the UA Summit, President Michael D. Higgins, patron of the Undergraduate Awards, presented the awards to the 39 winners at a ceremony at Royal Hospital Kilmainham on 9 November.