Arithmetic and Geometry of Algebraic Varieties

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