Mathematical Sciences: Linkage, Symmetric Algebras, and Hyperplane Sections

该奖项支持三个领域的研究， 代数 本研究的第一部分旨在研究 联动 首席研究员将研究一个数字 条件的分级分辨率，这可能意味着一个理想 是利西。 他还将研究几个 局部环的可能定义是licci。 第二 他的工作的一部分是关于对称代数的模块 Vasconcelos的阶乘猜想 他的第三部分 工作的目的是了解约化和不可约射影 曲线的一般超平面截面。 这在代数几何领域是合理的， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。 在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。 如今，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及理论计算机科学和机器人技术。

This award supports research in three areas of commutative algebra. The first part of this work is directed at studying linkage. The principal investigator will study a numerical condition on the graded resolution that might imply that an ideal is licci. He also will study the relation between several possible definitions for a local ring to be licci. The second part of his work is concerned with symmetric algebras of modules and Vasconcelos' Factorial Conjecture. The third part of his work is aimed at understanding reduced and irreducible projective curves in terms of their general hyperplane sections. This is reasearch in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. 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 from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and robotics.