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

SCEMS：数论、表示论和数学物理的计算前沿

• 批准号: 0821725
• 负责人: William Stein
• 金额: $ 10.69万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0821725&HistoricalAwards=false
• 关键词: SCREMS; Computational; Frontiers; Number; Theory

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.

该奖项将提供计算设备（服务器），以支持三个相关研究小组对表示论、数论和数学物理前沿的研究。表示论小组将计算所有秩为9的简单李群的Kazhdan-Lusztig-Vogan多项式，并将这些计算结果随时提供给世界各地的研究人员。数论组将进行模形式和L函数的主要计算，并大大提高我们对Birch和Swinnerton-Dyer猜想和Riemann假设的理解，数论中的两个中心问题。数学物理组将完成超对称的离壳表示分类的第一个主要步骤，这个问题已经存在了三十年。