The 2009 Graduate Student Combinatorics Conference; Spring 2009; Lexington, KY

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The proposal is to provide partial support for seventy-five graduate students and the keynote speaker Richard Stanley (MIT) to attend the 2009 Graduate Student Combinatorics Conference. The University of Kentucky is hosting this event. The twenty-four student research and expository talks and twenty-five posters at the poster sessions are a representative sampling of current trends in algebraic, geometric and topological combinatorics. The talk topics include: tropical oriented matroids, Coxeter graphs, k-Schur polynomials, permutation enumeration, Hopf algebras, non-crossing partition lattices, sporadic groups, the Rogers-Ramanujan identities, Hamiltonian decompositions of multigraphs, free and non-free hyperplane arrangements, energy of graphs and digraphs, the Monotone Column Permanent conjecture and k-parabolic subspace arrangments. The participants hail from leading combinatorics graduate programs in the United States and Canada. The results intersect work of researchers from a wide variety of areas of combinatorics, including Ardila and Develin, Babson and Steingrimsson, Barcelo, Billera and Brenti, Bressoud, Ehrenborg and Readdy, Fukuyama, Goulden and Jackson, Haglund, Knutson and Miller, and Stanley.This conference serves to give young researchers in combinatorics a welcoming medium to present their results, an opportunity to make new professional contacts, and a forum to showcase new results and trends in combinatorics. The field of combinatorics is a growing, vibrant and interdisciplinary area of mathematics. Combinatorialists use techniques from algebra, topology, geometry, and more recently, harmonic analysis and algebraic statistics to understand discrete structures. Combinatorial methods are applied to questions in the sciences, including those stemming from genetics, biology and physics. The GSCC will expose the participants to many of the new ideas, leading developments and techniques in combinatorics, will augment the mathematics they are currently seeing at their home institutions, and will continue to foster the interdisciplinary nature of the field of combinatorics. Additionally, the poster session will encourage greater networking and interaction among the participants and these new professional contacts may very likely result in future research projects.