Mathematical Sciences: Well-Partial-Ordering Theory and Ramsey Theory

该奖项支持芝加哥大学伊戈尔·克里兹教授在拉姆齐理论和图论方面的研究。克里兹博士提出结合拉姆齐理论来研究良偏序理论的主要问题。具体来说，他将尝试将Robertson-Seymour图小定理推广到无限图的情况，并将继续研究良偏序理论和Ramsey理论中的序数不变量。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 Ramsey theory and graph theory of Professor Igor Kriz of the University of Chicago. Dr. Kriz has proposed to study major questions of well-partial- ordering theory in connection with Ramsey theory. Specifically, he will attempt to generalize the Robertson-Seymour graph-minor theorem to the case of infinite graphs, and will continue his investigations of ordinal invariants in well-partial-ordering theory and Ramsey theory. 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.