Equations and Moduli of Abelian Surfaces, Free Resolutions, Smooth Small Codimensional Projective Varieties

波佩斯库9610205首席研究员将从事代数几何、计算代数和计算代数几何的研究。他将研究以下领域的问题：(1)阿贝尔曲面的Calabi-Yau 3-折叠、模和方程；(2)Coble-Gale变换和自由分解；(3)向量丛分解；(4)小余维光滑射影簇。计算方面涉及新的代数算法的设计及其在一些当前可用的系统中的实现：Macaulay、Macaulay2和Schubert。这是在代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。

Popescu 9610205 The principal investigator will pursue research in algebraic geometry, computational algebra, and computational algebraic geometry. He will work on problems in the following areas: (1) Calabi-Yau 3-folds, moduli and equations of abelian surfaces; (2) The Coble-Gale transform and free resolutions; (3) Vector bundle resolutions; and (4) Small codimensional smooth projective varieties. The computational aspects involve the design of new algebraic algorithms and their implementation in some of the currently available systems: Macaulay, Macaulay2 and Schubert. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, 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 physics, theoretical computer science, and robotics.