Mathematical Sciences: Hyperbolic Geometry and Nevanlinna Theory

数学科学：双曲几何和奈万林纳理论

• 批准号: 9626598
• 负责人: Pit-Mann Wong
• 金额: $ 6.82万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626598&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hyperbolic; Geometry; Nevanlinna

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.

9626598 Wong该提议在于几个复杂变量的一般区域，重点是Nevanlinna理论。更具体地说，研究人员将致力于非均等和更高维值的分布理论及其在复杂的超纤维性上的应用。与一个变量理论不同，较高的维值分布理论涉及复杂差分和代数几何形状的复杂工具，因此与数学科学中其他几个研究领域的接口。 由于Vojta发现了IT和Diophantine方程之间的类比，对Nevanlinna理论的兴趣最近以戏剧性的方式恢复了。二磷酸方程是整数中的方程式 - 数字理论的重要组成部分 - 正如费马特的最后一个定理所证明的那样，通常很难求解。 Vojta的发现表明，二磷剂方程的几个主要结果与Nevanlinna理论中的分析相似，并且两种理论之间可能存在隐藏的联系。