Mathematical Sciences: Algebraic Cycles on Varieties

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This project is concerned with the higher Chow groups of algebraic varieties over various fields. The principal investigator will study the kernel of the Albanese map for a smooth, projective surface over various fields. He will also consider the question of computing the torsion subgroup of CH2(X) when this is known to be finite. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics. In its origins, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays, the field makes use of methods not only from algebra, but analysis and topology. It is finding application in those fields as well as in theoretical computer science and robotics.