9401575 Stembridge This award funds the research of Professor John Stembridge into applications of combinatorial methods into problems of Algebra. The goal is to produce algorithmic methods for producing certain generating functions, enumerating reduced expressions obtained from studies of algebra, and constructing particular bases. The results should have applications in algebra, number theory and algebraic geometry. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting.
