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

该奖项支持拉姆齐理论和图的研究 芝加哥大学教授伊戈尔·克里兹的理论。博士 Kriz提出要研究井偏的主要问题- 排序理论与拉姆齐理论。具体地说， 他将尝试推广罗伯逊-西摩图子式 定理的情况下，无限图，并将继续他的 良偏序中序不变量的研究 Ramsey理论和Ramsey理论 这项研究福尔斯属于广义的组合学范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.

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.