Mathematical Sciences: Structure of Projective Modules and Generation of Ideals over Affine Rings

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This project is concerned with research in commutative algebra. The principal investigator will investigate the structure of projective modules and the efficient generation of ideals and modules over affine algebras. The goal is to study these problems by attaching suitable invariants to projective modules and ideals. These invariants arise from the geometry of the affine variety attached to the ring. A prominent role is played by the Chow groups of the affine varieties and the Chern classes of projective modules. This research is in the general area of algebraic geometry. Algebraic geometry is the study of geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics. It has widespread applications in mathematics, computer science and physics.