Mirror Symmetry and Modular Functions

连9619884这项研究是关于镜像对称和模函数的工作。首席研究员将致力于将环面超曲面的已知结果推广到环面完全相交的情况。他将尝试构建所有大半径极限点。他还将致力于将关于K3曲面的镜像映射的模性的工作扩展到任意的单参数族和多参数族。最后，他将研究K3-纤维三重的S对偶性。这是在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。

Lian 9619884 This research is concerned with work on mirror symmetry and modular functions. The principal investigator will work on extending known results for toric hypersurfaces to the case of toric complete intersections. He will try to construct all large radius limit points. He will also work on extending work on modularity of the mirror map for K3 surfaces to arbitrary 1-parameter families and to multiparameter families. Finally, he will study S-duality for K3-fibered threefolds. 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.