Mathematical Sciences: Arithmetic and Geometry of Automorphic Forms

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Professor Harris will work on several problems connected with the arithmetic and geometry of automorphic forms with a view towards applications to the theory of motives. In particular, he will study mixed motives arising from the cohomology of Shimura varieties especially those derived from unitary groups. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.