Conference: Southeastern Lie Theory Workshop Series

该项目支持参加东南李氏理论研讨会系列中的两个研讨会：“代数和应用的组合表示理论”(2023年5月12日至14日：北卡罗来纳州立大学)和“量子群、量子对称对及其分类”(2024年3月1日至3日，弗吉尼亚大学)。东南测谎理论联盟和研讨会系列将继续促进和加强美国东南部在测谎理论和代表性理论方面的区域研究合作。主要研究人员在研讨会上的专题说明性演讲将为研究生和职业生涯早期的研究人员提供一个加强他们研究计划的途径。会议期间的数学互动和指导机会将培养强大的区域研究和教育传统。拟议的工作坊广泛涉及李代数的表示理论、量子群和相关的代数结构。这些主题与理论物理、数论、代数几何和其他学科有许多联系。这些领域的研究涉及到对广泛的代数、组合或范畴对象的研究，其样本包括：量子化包络代数、量子函数代数、Kac-Moody李代数、Hecke代数、正则基和晶基、顶点算子代数、Hall代数、箭图、簇代数、Hopf代数和Khovanov-Lauda-Rouquier代数。一般而言，量子化Kac-Moody李代数的表示理论及其伴随的范畴和几何发展不仅在李理论中，而且在数学和物理的其他领域，如组合学、群论、数论、可积系统、低维拓扑和共形场论中都具有重要的作用。研讨会系列网站为https://www.math.lsu.edu/~pramod/selie/.2023年5月研讨会的网站是https://sites.google.com/ncsu.edu/selieworkshop2023.This奖，反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project supports participation in two workshops: "Combinatorial Representation Theory of Algebras and Applications" (May 12-14, 2023: North Carolina State University) and "Quantum Groups, Quantum Symmetric Pairs and their Categorifications" (March 1-3, 2024, University of Virginia) in the Southeastern Lie Theory Workshop Series. The Southeast Lie Theory Consortium and Workshop Series will continue to stimulate and enhance regional research collaboration in Lie theory and representation theory in the Southeastern United State. Featured expository talks at the workshops by leading researchers will provide an avenue for graduate students and early-career researchers to enhance their research programs. The opportunities for mathematical interactions and mentorship during the conferences will foster a strong regional tradition of research and education. The proposed workshops are broadly concerned with the representation theory of Lie algebras, quantum groups, and related algebraic structures. These topics have numerous connections to theoretical physics, number theory, algebraic geometry, and other disciplines. Research in these fields involves the study of a broad range of algebraic, combinatorial, or categorical objects, a sampling of which includes: quantized enveloping algebras, quantum function algebras, Kac--Moody Lie algebras, Hecke algebras, canonical bases and crystal bases, vertex operator algebras, Hall algebras, quivers, cluster algebras, Hopf algebras, and Khovanov-Lauda-Rouquier algebras. In general, the representation theory of quantized Kac--Moody Lie algebras and its accompanying categorical and geometric developments has taken on a significant role not only within Lie theory but also in other areas of mathematics and physics such as combinatorics, group theory, number theory, integrable systems, low-dimensional topology and conformal field theory. The workshop series website is https://www.math.lsu.edu/~pramod/selie/. The website for the May 2023 Workshop is https://sites.google.com/ncsu.edu/selieworkshop2023.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.