New Directions in Lie theory

该赠款将支持美国的数学家参加学期“新方向在李学理论”（http：//www.crm.math.ca/LieTheory2014/）将在中心德研究数学在蒙特利尔大学举行从2014年1月1日至6月30日;该奖项支持的第一个活动将于2014年1月6日至17日举行。 本专题学期的总体目标是突出当前在李学理论及其在其他领域的应用方面的研究。为此，将举办四次讲习班和四次小型课程。 迷你课程分为两个冬季学校，旨在帮助学生和博士后研究员利用讲习班。 研讨会将集中在最近的发展组合表示理论，霍尔和集群代数，数学物理和分类。 目的之一是突出这四种研究途径之间的联系。 例如，q-特征标的组合学在霍尔代数和簇代数以及分类中都很重要。 来自可积系统（如Q-系统）的思想对组合表示论和簇代数产生了重大影响。 每个研讨会的发言者都被选择来反映李学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有重要的应用，反过来，李理论也从这些联系中受益。 蒙特利尔大学数学研究中心以其专题学期、科学研讨会和外联活动而闻名于世，是加拿大数学基础研究及其应用的国家中心之一。 这笔赠款将促进国际合作，并增加美国和加拿大研究人员之间的联系。 与不同的数学家社区的互动将有助于年轻的数学家制定一个强大的研究计划。 他们将能够利用国际合作的机会。 在讲习班和/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。 来自美国的高级数学家和国际研究生之间的互动也将有助于扩大美国研究生课程的申请人数。

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.