Topics in arithmetic algebraic geometry

这位研究者和他的合作者和学生研究了算术几何中的几个主题，特别是与L级数自同构的特定值有关的Shimura簇上的圈的算术交理论。这是他以前在Gross-Zagier公式和Arakelov理论方面的工作的扩展。这是一个数学子领域的项目，称为数论。这些问题中的许多都是由这样的哲学驱动的，即代数信息可以通过几何方法获得。可以说，这项提议中问题的解决有朝一日会影响密码学、理论物理和量子计算的研究，这并不是太雄心勃勃。

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.