Mathematical Sciences: Free Resolutions in Commutative Algebra

这个项目是关于自由分辨率的。主要研究者将研究有限分辨率，特别强调它们可能支持的乘法结构及其在联系理论中的作用。解析族将被研究，包括对象的解析，如在一个完全交的连杆类中的代数，由残差交和完美理想的幂定义的代数，规范类和其他类群元素，以及固定维环上有限长度的模。代数几何是研究由多项式方程组的零点集合所产生的几何对象的学科。这是数学中最古老也是目前最活跃的分支之一。它在数学、计算机科学和物理学中有着广泛的应用。

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.