MATHEMATICAL SCIENCES: Homology Representations Arising FormPosets of Partitions and Subspace Arrangements

9400875 Sundaram该奖项资助Sheila Sundaram教授在代数组合学方面的研究。特别地，Sundaram教授将研究分拆格的子系同调.她将试图证明与某些偏序集相关的惠特尼同调模实际上是置换模。这一猜想对正切数和Genocchi数的精化有一定的影响。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。从根本上讲，组合学研究的是系统的计数和排列。当对象很难列出时，计算可能会非常困难，组合学家寻找克服这些困难的一般方法。今天的组合学利用了各种各样最先进、最现代的数学技术。虽然它的起源可以追溯到几个世纪前，但在过去的几十年里，这一领域得到了爆炸性的发展。这一增长来自于它在通信和信息技术中的重要性，以及从现代技术的成功到计算问题。***

9400875 Sundaram This award funds the research of Professor Sheila Sundaram in algebraic combinatorics. In particular Prof. Sundaram will the homology of subposets of the partition lattice. She will try to establish that Whitney homology modules associated to certain posets are in fact permutation modules. This conjecture has implications regarding refinements of the tangent and Genocchi numbers. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting and arrangement. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting. ***