Conference: Southeastern Lie Theory Workshop Series

该项目支持参加两个研讨会："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）在东南部李理论研讨会系列。东南谎言理论联盟和研讨会系列将继续刺激和加强在谎言理论和表征理论在美国东南部的区域研究合作。由领先的研究人员在研讨会上进行的专题演讲将为研究生和早期职业研究人员提供一个途径，以加强他们的研究计划。会议期间的数学互动和指导机会将促进研究和教育的强大区域传统。 拟议的研讨会广泛关注李代数，量子群和相关的代数结构的表示理论。 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。 在这些领域的研究涉及广泛的代数，组合，或分类对象的研究，其中的抽样包括：量子包络代数，量子函数代数，卡茨-穆迪李代数，赫克代数，规范基地和晶体基地，顶点算子代数，霍尔代数，箭图，集群代数，霍普夫代数，和Khovanov劳达Rouquier代数。在一般情况下，表示理论的量化卡茨-穆迪李代数及其伴随的范畴和几何的发展已采取了显着的作用，不仅在李理论，而且在其他领域的数学和物理，如组合，群论，数论，可积系统，低维拓扑和共形场论。研讨会系列网站是www.example.com。2023年5月研讨会的网站是www.example.com奖项反映了NSF的法定使命，并被认为值得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来支持。

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.