Mathematical Sciences: Geometry of Automorphic Forms

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This award supports the research of Professor Michael Harris, who will continue to study the arithmetic and geometry of automorphic forms and representations of p-adic groups. Harris intends to explore the relations of recent developments in the field to special values of automorphic L-functions. He will also continue working on applications of this work to the representation theory of p-adic groups. Further, he will complete projects related to the mixed motives arising in the cohomology of Shimura varieties. 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.