Mathematical Sciences: Free Resolutions in Commutative Algebra

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This project is concerned with free resolutions. The principal investigators will study finite resolutions, with particular emphasis on the multiplicative structures they may support and their role in linkage theory. Families of resolutions will be investigated including resolutions of objects such as algebras in the linkage class of a complete intersection, algebras defined by residual intersections and powers of perfect ideals, canonical classes and other class group elements, and modules of finite length over rings of a fixed dimension. Algebraic geometry is the study of the 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.