Mathematical Sciences: Algebraic Combinatorics

该奖项支持密歇根大学安娜堡分校的Philip Hanlon教授在组合学方面的研究。Hanlon博士将在组合学和表示理论的交汇处研究两个一般问题领域。第一部分讨论了某些幂零李代数的同调性，以及对麦克唐纳根猜想的同调扩展。第二个领域涉及与Jones的基本构造有关的问题，以及与Stanley的斐波那契r微分偏置集相对应的Brauer的集中代数的代数结构。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表了对所有数学活动——计数——的系统化。然而，在其现代发展中，组合学已经不仅仅是计算，而是利用了各种各样的先进数学技术，尽管它的根源可以追溯到几个世纪以前，但由于它在通信和信息技术中的重要性，该领域在过去的几十年里有了爆炸性的发展。

This award supports the research in Combinatorics of Professor Philip Hanlon of the University of Michigan at Ann Arbor. Dr. Hanlon will work in two general problem areas at the junction of Combinatorics and Representation Theory. The first area is concerned with the homology of certain nilpotent Lie algebras, and homological extensions to the Macdonald root- system conjectures. The second area is concerned with problems related to Jones's basic construction, and the algebra structures of Brauer's centralizer algebras corresponding to Stanley's Fibonacci r-differential posets. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, Combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.