New Directions in Lie theory

该资助将支持美国数学家参加于2014年1月1日至6月30日在蒙特利尔大学数学研究中心举行的学期“李理论新方向”（http://www.crm.math.ca/LieTheory2014/）；该奖项支持的第一项活动将于2014年1月6日至17日举行。主题学期的总体目标是突出李理论的研究现状及其在其他领域的应用。这将通过举办四个讲习班和四个迷你课程来实现。迷你课程分为两个冬季学校，旨在为学生和博士后准备利用研讨会。讲习班将集中讨论组合表示理论、霍尔代数和聚类代数、数学物理和分类的最新发展。目的之一是强调这四种研究途径之间的联系。例如，q字符的组合学在霍尔代数和聚类代数以及分类中都很重要。来自可积系统的思想，如q系统，对组合表示理论和聚类代数产生了重大影响。每个研讨会的演讲者都被选择来反映李理论中这些不同方向之间的协同作用。李论是当代数学的一个中心领域。李群和李代数的结构和表示理论在物理学和其他数学分支中得到了重要的应用，而李论也从这些联系中受益。蒙特利尔大学数学研究中心以其主题学期、科学研讨会和推广活动而闻名于世，是加拿大数学及其应用基础研究的国家中心之一。这项资助将促进国际合作，并增加美国和加拿大研究人员之间的联系。与不同数学家群体的互动将有助于年轻数学家发展强大的研究计划。他们将能够利用国际合作的机会。在研讨会和/或专题研讨会上发言的机会将有助于他们向高级数学家传播他们的工作。这也将有助于他们申请经常需要当地导师的国际博士后职位。美国高级数学家与国际研究生之间的互动也将有助于扩大美国研究生项目的申请范围。

The grant will support US based mathematicians to participate in the semester "New Directions in Lie theory" (http://www.crm.math.ca/LieTheory2014/) to be held at the Centre de Recherches Mathematiques at the University of Montreal from January 1 to June 30, 2014; the first activity supported by this award will take place January 6--17, 2014. The overall goals of the thematic semester is to highlight the current research in Lie theory and its applications to other fields. This will be achieved by having four workshops and four mini-courses. The mini-courses are split into two winter schools and are designed to prepare students and postdoctoral fellows to take advantage of the workshops. The workshops will focus on recent developments in combinatorial representation theory, Hall and cluster algebras, mathematical physics and categorification. One of the aims is to highlight the connections between these four avenues of research. For instance, the combinatorics of q-characters has been important in both Hall and cluster algebras and categorification. The ideas coming from integrable systems, such as the Q-systems, has had a major impact on combinatorial representation theory and cluster algebras. The speakers of each workshop have been chosen to reflect the synergy between these different directions in Lie theory. Lie theory is a central area of contemporary mathematics. The structure and representation theory of Lie groups and Lie algebras have resulted in important applications in physics and other branches of mathematics and, in turn, Lie theory has benefited from these connections. The Centre de Recherches Mathematiques at the University of Montreal is world renowned for its thematic semesters, scientific workshops and outreach activities and is one of Canada's national centers for fundamental research in mathematics and their applications. This grant will foster international collaborations and to increase connections between US and Canadian researchers. The interactions with a diverse community of mathematicians will help young mathematicians to develop a strong research program. They will be able to take advantage of the opportunities for international collaborations. The opportunity to speak at the workshop and/or the thematic seminar will help them to disseminate their work to senior mathematicians. This will also help them to apply for international postdoctoral positions which frequently need a local mentor. The interactions between the senior mathematicians from the US and international graduate students will also help to broaden the pool of applications to US graduate programs.