Mathematical Sciences: Some Problems (mostly) on Finite Sets

该奖项支持罗格斯大学杰弗里·卡恩教授在组合学方面的研究。卡恩博士将在以下主题进行研究：超图(有限集合的集合)的性质；给出n阶随机方阵(其中所有项都是0或1)的概率的良好估计的问题；以及关于有限布尔代数中理想中的相交族的Chvtal猜想。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，组合学代表着对所有数学活动中的第一项--计数--的系统化。然而，在它的现代发展中，组合数学已经不仅仅是计数，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前，但由于它在通信和信息技术中的重要性，该领域在过去几十年里有了爆炸性的发展。

This award supports the research in combinatorics of Professor Jeffry Kahn of Rutgers University. Dr. Kahn will be conducting investigations in the following topics: the properties of hypergraphs (collections of finite sets); the problem of giving a good estimate of the probability that a random square matrix of order n, in which all entries are zero or 1, should be singular; and Chvatal's conjecture on intersecting families in ideals in finite Boolean algebras. 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.