Mathematical Sciences: Kloosterman Sums and p-adic Differential Equations

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This award supports the research in Algebraic Geometry of Dr. Richard Crew of the University of Minnesota. His research will center on the study of Kloosterman sums by geometric methods, and in particular, he will investigate the monodromy groups arising from certain p-adic differential equations that come from these sums. This research is work in the Algebraic Geometry of finite characteristic. Although the field originated with notions of continuously varying geometric structures like lines and planes, in this context the Discrete takes over, and methods akin to those from the theory of whole numbers are most useful. Reciprocally, the algebraic geometry of finite characteristic is now having great influence on the Theory of Numbers, and is finding application in Computer Science and Coding Theory.