Mathematical Sciences: "Ascending/Descending Chain Conditions for Varieties with Log Canonical Singularities"

阿列克谢耶夫教授将研究具有对数正则奇点的品种。 特别是他打算工作的有界性定理在3维的情况下，试图推广工作的川俣和森有界性的法诺品种。 这是代数几何领域的研究。 代数几何本身是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。 在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。

Professor Alexeev will study varieties with log canonical singularities. In particular he intends to work on boundedness theorems in the 3-dimensional case in an attempt to generalize work of Kawamata and Mori on boundedness of Fano varieties. This is research in the field of algebraic geometry. Algebraic geometry itself 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.