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

该项目将支持2014年6月在北卡罗莱纳州立大学举行的为期五天的CBMS会议，主题是“Kac-Moody代数的高等表示理论”，由Raphael Rouquier担任主要发言人。Kac-Moody李代数及其量子类似物的理论是一个及时的主题，在数学和理论物理的其他分支中有各种应用。主要的发展集中在分类程序上，它根据基于组合、代数或几何结构的模块类别来实现关键的代数结构，如规范基。分类可以加深对原始代数结构的理解，从而获得新的代数结构。在量子包络代数的分类中，Khovanov-Lauda和Rouquier分别引入了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绘制可能的未来方向。会议结束后，Rouquier教授还将撰写CBMS讲座专著。会议预计将聚集约40名与会者。我们还邀请了另外五位演讲者来协助Rouquier教授讲解分类和高级表征理论。会议将鼓励妇女、少数民族和残疾人参与。

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.