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

“量子仿射代数与簇代数、当前代数和分类的相互作用”会议将于2018年6月2日至8日在华盛顿特区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有关或由其引起的问题。这些主题最近的快速增长、日益突出和新兴的联系强调了及时召开一次会议的必要性，该会议通过汇集在这些主题的不同方面工作的主要研究人员来关注新的联系。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，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/讲习班。无限维李代数及其量子类似物在数学和数学物理中占有重要地位。近几十年来，他们的表示理论与许多不同的学科联系在一起，如代数几何、代数拓扑、组合学和聚类代数，仅举几例。讲座将集中在晶体和正则基，Weyl， Demazure和Kirillov-Reshetikhin模块及其相互作用，最高权范畴，Khovanov-Lauda-Rouquier代数及其在分类中的应用，聚类代数和相关结构，无限维表示理论中的几何方法（特别是颤振变体的作用）和映射代数等主题上。将特别强调各种结构之间的相互作用。更多的细节可以在会议网站上找到：http://www.mi.uni-koeln.de/~dkus/.This该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

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.