SCREMS: The Computational Frontiers of Number Theory, Representation Theory, and Mathematical Physics

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This award will provide computational equipment (servers) which would support research by three related groups of researchers into the frontiers of Representation Theory, Number Theory, and Mathematical Physics.The Representation Theory group will compute the Kazhdan-Lusztig-Vogan polynomials for all simple Lie groups up to rank 9 and make the results of these computations readily available to researchers worldwide. This group will also continue to explore the combinatorial infrastructure of W-graphs and relate it to representation theoretical invariants.The Number Theory group will carry out major computations of modular forms and Lfunctions, and greatly enhance our understanding of the Birch and Swinnerton-Dyer conjecture and the Riemann Hypothesis, two of the central problems in number theory.The Mathematical Physics group will complete the first major step in the classification of off-shell representations of Supersymmetry, a problem that has been open for three decades.