Mathematical Sciences: Complex Hyperbolicity, Value Distribution Theory and its Relation with Diophantine Approximation

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9506424 Ru The proposed research lies in the interface of number theory and several complex variables. It seeks to understand the somewhat mysterious relationship between Nevanlinna theory and diophantine geometry. In particular, the investigator proposes to give a single proof for the second main theorem in Nevanlinna theory and the Roth-Schmidt-Faltings theorem in diophantine geometry. Recently, formal analogies between certain areas of complex geometry and number theory have been observed. This is exciting in that on the face of it these are two totally unrelated areas of mathematics: number theory deals with integer equations whereas complex geometry deals with non-discrete objects.