Higher Dimensional Geometry

计划研究的领域是高维代数几何，特别是最小模型程序和Mori理论。在之前工作的基础上，一些问题集中在对数范畴（有边界的投影变化），特别是关于log del Pezzo曲面和变形理论的工作。提出了高维代数几何中的一些更一般的问题。这是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，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

McKernan The area of the planned research is in higher dimensional algebraic geometry, more especially the minimal model program and Mori theory. Building on previous work, some questions centered around the log category (projective varieties with boundaries), especially work on log del Pezzo surfaces and deformation theory. Some more general problems in higher dimensional algebraic geometry are also proposed. 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.