Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

量子仿射代数与簇代数、现代数和分类的相互作用

• 批准号: 1810211
• 负责人: Prasad Senesi
• 金额: $ 4.92万
• 依托单位: Catholic University of America
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-05-15 至 2019-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1810211&HistoricalAwards=false
• 关键词: Interactions; Quantum; Affine; Algebras; Cluster

The conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification" will take place at the Catholic University of America in Washington, DC on June 2-8, 2018. The conference will focus on problems related to, or motivated by, representations of infinite dimensional Lie algebras and their quantum analogues. The recent rapid growth, rising prominence, and emerging connections between these topics underscores the timely need for a conference that focuses on new connections by bringing together leading researchers who work on different aspects of these subjects. A main goal of the conference is to expose graduate students and early-career researchers to recent developments in representation theory. In an effort to foster their interest and engagement, the four day conference will be preceded by a three day summer school/workshop for junior researchers. Infinite-dimensional Lie algebras and their quantum analogues play a prominent role in mathematics and mathematical physics. In recent decades their representation theory has been connected with a number of different subjects, such as algebraic geometry, algebraic topology, combinatorics and cluster algebras, to name but a few. The talks will focus on topics such as crystal and canonical bases, Weyl, Demazure and Kirillov-Reshetikhin modules and interaction between them, highest weight categories, Khovanov-Lauda-Rouquier algebras and their applications to categorification, cluster algebras and related structures, geometric methods in infinite dimensional representation theory (in particular, the role of quiver varieties), and map algebras. A special emphasis will be placed on interactions between various structures. Further details can be found at the conference website: http://www.mi.uni-koeln.de/~dkus/.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.

会议“量子仿射代数与集群代数，当前代数和分类的相互作用”将于2018年6月2日至8日在华盛顿的美国天主教大学举行。会议将集中讨论与无限维李代数及其量子类似物的表示相关或受其启发的问题。最近的快速增长，日益突出，以及这些主题之间的新兴联系，强调了及时需要一个会议，重点是通过汇集在这些主题的不同方面工作的领先研究人员的新联系。会议的一个主要目标是让研究生和早期职业研究人员了解表征理论的最新发展。为了培养他们的兴趣和参与度，为期四天的会议之前将为初级研究人员举办为期三天的暑期学校/研讨会。无限维李代数及其量子类似物在数学和数学物理中起着重要作用。近几十年来，他们的代表性理论已连接到一些不同的主题，如代数几何，代数拓扑，组合和集群代数，仅举几例。会谈将集中在主题，如晶体和规范基地，外尔，Demazure和Kirillov-Reshetikhin模块和它们之间的相互作用，最高权重类别，Khovanov-Lauda-Rouquier代数及其应用分类，集群代数和相关结构，几何方法在无限维表示理论（特别是，的作用，品种），和地图代数。将特别强调各种结构之间的相互作用。更多细节可在会议网站上找到：http://www.mi.uni-koeln.de/~dkus/.This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。