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

9506424 Ru提出的研究是数论与几个复变量的接口。它试图理解奈万林纳理论和丢番图几何之间有些神秘的关系。特别地，研究者建议对Nevanlinna理论中的第二个主要定理和丢芬图几何中的Roth-Schmidt-Faltings定理给出一个单一的证明。最近，在复杂几何和数论的某些领域之间的形式化类比已经被观察到。这很令人兴奋，因为从表面上看，这是两个完全不相关的数学领域：数论处理整数方程，而复杂几何处理非离散对象。

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.