Mathematical Sciences: Algebraic Combinatorics

该奖项支持菲利普·汉伦教授在代数组合学领域的研究。Hanlon将研究与两个不同主题相关的一些问题，即Macdonald Root System猜想和Varchenko在其关于量子群表示和与量子群相关的超几何函数的工作中定义的内积矩阵。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究离散的对象集合如何排列。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如那些发生在电话系统中的网络，以及计算机科学中的算法设计，都涉及离散的对象集，这利用了组合研究。

This award supports the research of Professor Philip Hanlon in the field of algebraic combinatorics. Hanlon will investigate a number of problems connected with two distinct subjects, the Macdonald Root System Conjectures and the inner product matrices defined by Varchenko in his work on representations of quantum groups and hypergeometric functions related to quantum groups. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.