Mathematical Sciences: Two Problems in Modular Surfaces

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Professor Sheingorn will work on several problems connected with automorphic forms. In particular, he will study the consequences of the insight that certain number theoretic objects are equivalent to geometric traits of geodesics on highly symmetric spaces. 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.