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

该奖项将提供计算设备（服务器），以支持三个相关研究小组在表示理论、数论和数学物理领域的研究。表示理论小组将为所有9级以下的简单李群计算Kazhdan-Lusztig-Vogan多项式，并使这些计算结果随时可供全世界的研究人员使用。该小组还将继续探索w图的组合基础结构，并将其与表示理论不变量联系起来。数论小组将进行模形式和l函数的主要计算，并大大提高我们对Birch和Swinnerton-Dyer猜想以及黎曼假设这两个数论中心问题的理解。数学物理小组将完成超对称脱壳表示分类的第一步，这是一个已经开放了30年的问题。

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.