Topics in arithmetic algebraic geometry

研究者和他的合作者和学生研究算术几何中的几个主题，特别是与L-级数的自守的特殊值有关的志村簇上的循环的算术交集理论，扩展了他以前在Gross-Zagier公式和Arakelov理论上的工作。这是数学的一个子领域，称为数论的项目。这些问题中有许多是由这样一种哲学所激发的，即代数信息可以通过几何方法来获得。 可以毫不夸张地说，这个提案中的问题的解决方案有一天会影响密码学、理论物理学和量子计算的研究。

The investigator and his collabortaors and students study several topics in arithmetic geometry, in particular to arithmetical intersection theory of cycle on Shimura varieties with connection to special values of automorphic of L-series extending his previous work on the Gross-Zagier formula and Arakelov theory.This is a project in a subfield of mathematics known as number theory. Many of these questions are motivated by the philosophy that algebraic informations can be obtained by geometric methods. It is not too ambitious to say that the solution to the problems in this proposal will one day affect research in cryptography, theoretic physics, and quantum computing.