Groups Representations and Applications: New Perspectives

群论本质上是数学和物理系统的对称理论，它是现代纯数学的基础，与物理、化学和信息科学有着重要的联系。特别是在完成了有限简单群的分类（CFSG）之后，在拓扑学、代数几何、李论、同调代数和数学物理等领域的重要而深刻的联系被发现和利用。尽管如此，这一领域仍充斥着基本问题和长期存在的猜想。最近的突破显示出最终解决一些古老的开放性问题的前景。反过来，群和表示理论的最新成果导致了李论、数论、代数几何、组合学和半群理论的大量应用取得了实质性进展。所有这些丰富的新结果和新方向将成为2020年为期六个月的“群体、表现和应用：新视角”项目的主题，该项目将于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）举行，其中包括五个为期一周的研讨会。这个项目的目标是将群理论和表示理论领域的顶尖专家，以及其他几个关键数学领域的专家聚集在一起，解决一些主要问题，并将CFSG与其他数学领域之间的许多联系提升到一个新的水平。详细信息请参见该计划的网站http://www.newton.ac.uk/event/gra。该赠款提供的资金将支持该项目内五个为期一周的讲习班的美国参与者。该奖项反映了美国国家科学基金会的法定使命，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。

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.