Topics in Algebraic Geometry and Number Theory

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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.