This award supports the research of Professors Richard Stanley and Gian-Carlo Rota in Combinatorics and its connections with other areas of mathematics. Professor Stanley will work on extending his earlier research on polytopes, Hilbert functions, symmetric functions, the monotone triangle conjecture, and differential posets. Professor Rota will work on invariant theory, geometric probability, umbral calculus, and the theory of species. 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.
