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.
