Mathematical Sciences: Combinatorial Aspects of Representation Theory & the Theory of Symmetric Functions

该奖项支持A. Garsia教授在组合学方面的研究。他打算研究有限反射群的表示，特别是通过研究麦克唐纳基而得出的问题。他还将研究轨道谐波和梯度表示以及梯度模块的q，t-Kostka系数。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散的对象集合。因此，它对现代通信非常重要，例如电话系统中大型网络的设计以及计算机科学中算法的设计。

This award supports the research of Professor A. Garsia to work in combinatorics. He intends to investigate representations of finite reflection groups, in particular, problems derived from studying the Macdonald basis. He will also study orbit harmonics and graded representations and the q,t-Kostka coefficients of bigraded modules. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it is extremely important to modern communications, for example the design of large networks as in telephone systems and the design of algorithms in computer science.