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），支持三个相关研究小组对表示论、数论和数学物理前沿领域的研究。表示论小组将计算所有简单李的 Kazhdan-Lusztig-Vogan 多项式分组最高可达 9 级，并使全世界的研究人员可以轻松获得这些计算结果。该小组还将继续探索W图的组合基础设施，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，并极大地增强我们对Birch和Swinnerton-Dyer猜想的理解和黎曼猜想，数论中的两个核心问题。数学物理小组将完成超对称离壳表示分类的第一个重要步骤，这个问题已经被解决了。开放了三十年。