Topics in arithmetic algebraic geometry

Columbia University, New York NY

Investigators

Abstract

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.