Mathematical Sciences: Hyperbolic Geometry and Nevanlinna Theory

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9626598 Wong This proposal lies in the general area of several complex variables, with an emphasis on Nevanlinna theory. More specifically, the investigator will work on non-equidimensional and higher dimensional value distribution theory and its applications to complex hyperbolicity. Unlike the one variable theory, higher dimensional value distribution theory involves sophisticated tools from complex differential and algebraic geometry, hence interfaces with several other areas of research within mathematical sciences. Interest in Nevanlinna theory was recently revived in a dramatic way with Vojta's discovery of the analogies between it and Diophantine equations. Diophantine equations are equations in integers - an important part of Number Theory - and as evidenced by Fermat's Last Theorem are often very difficult to solve. Vojta's discovery indicates that several major results in Diophantine equations parallel those in Nevanlinna theory and that there may be hidden connections between the two theories.