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 这个建议涉及几个复变量的一般领域，重点是 Nevanlinna 理论。更具体地说，研究人员将致力于非等维和高维值分布理论及其在复杂双曲性中的应用。与单变量理论不同，高维值分布理论涉及复杂微分几何和代数几何的复杂工具，因此与数学科学中的其他几个研究领域相结合。 最近，随着沃伊塔发现内万林纳理论与丢番图方程之间的类比，人们对内万林纳理论的兴趣以戏剧性的方式重新燃起。丢番图方程是整数方程——数论的重要组成部分——并且正如费马大定理所证明的那样，通常很难求解。沃伊塔的发现表明丢番图方程中的几个主要结果与内万林纳理论中的结果相似，并且这两个理论之间可能存在隐藏的联系。