Mathematical Sciences: Free Resolutions in Commutative Algebra

该奖项支持交换代数中自由分辨率的研究。主要研究者将研究Vasconcelos的一个猜想，小连接数环上模的Poincare级数和betti数的渐近行为，tor代数中的高阶乘法，以及一般外乘法的核。本研究涉及交换代数和代数几何中的若干问题。代数几何研究多项式方程族的解。人们既可以研究解集的几何，也可以通过研究解集上的某些函数来代数地解决问题，这些函数形成了所谓的交换环。这种对偶视角在交换代数和代数几何之间建立了紧密的联系。

This award supports research on free resolutions in commutative algebra. The principal investigator will study a conjecture of Vasconcelos, the Poincare series and asymptotic behavior of betti numbers of modules over rings with small linking number, higher order multiplication in Tor-algebras, and the cokernel of generic exterior multiplication. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.