Rational Curves on Calabi-Yau Manifolds & Linear Series

徐教授将研究Calabi-Yau流形以及高维射影簇的几何和拓扑。特别是，他想研究Calabi-Yau三重有理曲线。他还打算研究高维射影簇上的伴随线性级数和多元正则级数。最后，他打算研究更高维的球体包装问题。这是代数几何领域的研究，但它与本世纪理论物理的两大进步--量子力学和广义相对论--直接相关。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。

Professor Xu will work on the geometry and topology of Calabi-Yau manifolds as well as higher dimensional projective varieties. In particular, he wants to study rational curves on Calabi-Yau threefolds. He also intends to work on adjoint linear series and pluricanonical series on projective varieties of higher dimension. Finally, he intends to work on higher dimensional sphere-packing problems. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. 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.