Mathematical Sciences: Intersection Theory Problems from Mathematical Physics

9500938童教授将研究更深入研究交集理论和模空间所衍生的问题。他希望用更代数的方法研究Teichmuller空间上某些向量丛上的平坦射影联络。他还希望研究数学物理中研究的BRST微分和切赫-科祖尔复合体之间的联系。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。***

9500938 Tong Professor Tong will study problems that derive from the deeper study of intersection theory and moduli spaces. He hopes to study more algebraically the flat projective connections on certain vector bundles over Teichmuller space. He also wishes to study the connections between the BRST differential studied in mathematical physics and the Cech-Koszul complex. 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. ***