Arithmetic and Geometry of Algebraic Varieties

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

The project addresses questions concerning the distribution of rational and integral points on higher dimensional algebraic varieties. The main problem is to relate the Zariski density and the asymptotic distribution of points to global geometric invariants. Number theory is one of the oldest branches of mathematics. Today it is marked by profound connections to geometry and analysis. It has a wide range of applications to data transmission, storage and cryptography. For example, many algorithms are based on arithmetic properties of elliptic curves. This research explores the higher dimensional case of surfaces and threefolds.