Groups Representations and Applications: New Perspectives

群体表示和应用：新视角

• 批准号: 1907670
• 负责人: Pham Tiep
• 金额: $ 2.5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-11-15 至 2023-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907670&HistoricalAwards=false
• 关键词: Groups; Representations; Applications; New; Perspectives

Group Theory is essentially the theory of symmetry for mathematical and physical systems, which underpins much of modern pure mathematics, with major connections to physics, chemistry, and information science. Especially after the completion of the Classification of Finite Simple Groups (CFSG), important and deep connections to areas as varied as topology, algebraic geometry, Lie theory, homological algebra, and mathematical physics, have been discovered and exploited. Still, the area abounds with basic problems and long-standing conjectures. Recent breakthroughs hold out the prospect of finally solving some venerable open problems. In turn, recent results in group- and representation theory have led to substantial progress in a vast number of applications in Lie theory, number theory, algebraic geometry,combinatorics and semigroup theory.All this wealth of new results and directions will be the main theme of the 2020 six-month program "Groups, Representations and Applications: New Perspectives", Jan. 6 - June 30, 2020, at the Isaac Newton Institute for Mathematical Sciences (INI, Cambridge, UK), which features five one-week workshops. The goal of this program is to bring together the leading experts in group and representation theory, on the one hand, and from several key other parts of mathematics on the other, to tackle some of the main problems and to take the many connections between CFSG and other areas of mathematics to the next level. Detailed information is given at the program's website http://www.newton.ac.uk/event/gra. Funding provided by the grant will support US-based participants of the five one-week workshops within the program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

群论本质上是数学和物理系统的对称性理论，它是现代纯数学的基础，与物理学，化学和信息科学有着重要的联系。特别是在有限单群分类（CFSG）完成之后，拓扑学、代数几何、李论、同调代数和数学物理等领域的重要和深刻联系被发现和利用。尽管如此，该地区仍然存在许多基本问题和长期存在的问题。最近的突破为最终解决一些悬而未决的古老问题提供了前景。反过来，最近在群和表示理论方面的研究成果也为李论、数论、代数几何、组合学和半群理论的大量应用带来了实质性的进展。所有这些丰富的新结果和方向将成为2020年为期六个月的计划"群、表示和应用：新视角"，2020年1月6日至6月30日，在艾萨克·牛顿数学科学研究所（INI，剑桥，英国），其中包括五个为期一周的研讨会。该计划的目标是一方面汇集群和表示论方面的领先专家，另一方面，从数学的其他几个关键部分，以解决一些主要问题，并将CFSG和其他数学领域之间的许多联系提升到一个新的水平。详细信息可在该计划的网站www.example.com上查阅。该基金会提供的资金将用于资助该计划中五个为期一周的研讨会的美国参与者。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。