Mathematical Sciences: Intersection Theory Problems from Mathematical Physics

小行星9500938 童教授将研究从交叉理论和模空间的深入研究中衍生出来的问题。他希望更多地研究代数平坦的射影连接某些向量丛超过Teichmuller空间。他还希望研究数学物理中研究的BRST微分和Cech-Koszul复体之间的联系。 这是代数几何领域的研究，但它直接关系到本世纪理论物理学的两个重大进展--量子力学和广义相对论。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，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。 ***

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. ***