NSF/CBMS Regional Conference on Higher Representation Theory-June 19-23, 2014

该项目将支持2014年6月在北卡罗来纳州立大学举行的为期五天的以“Kac-Moody代数的更高表示理论”为题的建立信任措施会议，主讲人是Raphael Rouquier。Kac-Moody李代数及其量子模拟的理论是一个适时的话题，在数学和理论物理的其他分支中有着广泛的应用。主要的进展集中在实现关键代数结构的分类程序上，例如标准基，根据基于组合、代数或几何结构的模块范畴。范畴化可以加深对原有代数结构的理解，获得新的结构。在量子包络代数的分类中，Khovanov-Lauda和Rouquier独立地引入了KLR代数。作为该领域的发明者和主要实践者之一，Rouquier教授将就该主题进行十次讲座，旨在向包括研究生在内的研讨会参与者介绍当前的研究并规划未来可能的方向。鲁奎尔教授还将在会议结束后撰写一部关于建立信任措施讲座的专著。这次会议预计将有大约40人参加。另外五位演讲者被邀请协助鲁奎尔教授的讲座，并谈论范畴化和更高表征理论。大会将鼓励妇女、少数群体和残疾人参加。

This project will support a five-day CBMS conference on "Higher representation theory of Kac-Moody algebras" at North Carolina State University in June 2014 with Raphael Rouquier as the principal speaker. The theory of Kac-Moody Lie algebras and their quantum analogs is a timely topic with various applications to other branches of mathematics and theoretical physics. Major developments have been focused on the categorification program which realizes key algebraic structures, such as canonical bases, in terms of category of modules based on combinatorial, algebraic or geometric structures. Categorification can provide deeper understanding of the original algebraic structures and obtain new structures. In categorification of quantum enveloping algebras, Khovanov-Lauda and Rouquier independently introduced the KLR algebra. As one of the inventors and a leading practitioner in this field, Professor Rouquier will give ten lectures on the subject which aim to introduce workshop participants, including graduate students, to current research and chart possible future directions. Prof. Rouquier will also write up a monograph of the CBMS lectures after the conference. The conference expects to gather about 40 participants. An additional five speakers are invited to assist Professor Rouquier's lectures and to talk about categorification and higher representation theory. The conference will encourage participation from women, minorities, and persons with disabilities.