Topics in Algebraic Geometry and Number Theory

这项研究项目将解决两个经典数学领域之间的当前感兴趣的主题：代数几何和数论。潜在的研究方法包括热带几何的思想，特别是将本学科的新基础应用于代数几何中的公开问题；或应用p-进解析几何来研究椭圆曲线和其他代数簇的L函数的值。这个项目横跨EPSRC的投资组合领域“数论”、“代数”和“几何与拓扑”，所有这些都属于数学科学主题。

This research project will address topics of current interest at the interface between two classical mathematical fields: algebraic geometry and numbertheory. Potential research methods include ideas from tropical geometry, particularly applications of the new foundations of this subject to open problems in algebraicgeometry; or applications of p-adic analytic geometry to studying values of L-functions for elliptic curves and other algebraic varieties. This project spans the EPSRC portfolio areas "number theory", "algebra", and "geometry & topology", all lying within theMathematical Sciences theme.