EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics

这个项目的目标是培养本科生、研究生和博士后在组合学、几何和表示理论的研究界面上。这一领域包括计数几何、无限维李代数的几何表示理论、相应的量子化泛包络代数和Hecke代数。在组合方面，我们还将重点介绍代数组合学及其应用。在过去的十年里，所有这些领域都取得了令人瞩目的进展。这项计划将在研究生、本科生和博士后的积极参与下进行。这些数学领域与数学物理(理论物理的数学方面)的许多最新发展密切相关，主要与量子场论、弦理论和统计力学有关。将要解决的组合问题在生物学中也有直接的应用，例如在系统发育树的研究中。这笔赠款(与其他赠款一起)将用于资助一些针对博士后研究员、研究生和本科生的热门研究主题的培训讲习班和大师班。

The goal of this project is training of undergraduate students, graduate students, and postdocs at the research interface of combinatorics, geometry, and representation theory. This area includes enumerative geometry, geometric representation theory of infinite dimensional Lie algebras, corresponding quantized universal enveloping algebras, and of Hecke algebras. On the combinatorial side we will also focus on algebraic combinatorics and its applications. All these areas have seen fascinating progress in the last decade.The project will be conducted with active involvement of graduate and undergraduate students and post-docs. These areas of mathematics are closely related to many recent developments in mathematical physics (the mathematical side of theoretical physics), mostly to quantum field theory, string theory, and statistical mechanics. Combinatorial problems which will be addressed also have direct applications in biology, for instance in the study of phylogenetic trees. This grant (in combination with other grants) will be used to fund a number of training workshops and master-classes on hot research topics aimed at post-doctoral fellows, graduate, and undergraduate students.