The Combinatorics & Asymptotics of Sequences of Characters of Symmetric Groups

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9401197 Regev This award funds the research of Prof. Amitai Regev in algebraic combinatorics. Prof. Regev will study the asympotics of character sequences, PI algebras and Kronecker products. This work has implication for combinatorics, representation theory and algebra. 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.