Mathematical Sciences: The Topology of Varieties

Hain打算利用Hodge理论的技巧来研究紧黎曼曲面空间的拓扑和复数上n×m矩阵空间的拓扑，所有n×m矩阵的子式都不为零。可能的应用包括构造满足Abel五项函数方程的自然推广的Euler双对数的推广。一名研究生将使用海恩编写的一个计算机程序来帮助研究双对数。该程序分解对称群的表示，对称群以巨大的张量积的形式出现。一台高性能的个人计算机将致力于这项任务。

Hain intends to use the techniques of Hodge theory to study the topology of the space of compact Riemann surfaces and the topology of the space of n x m matrices over the complex numbers, all of whose minors are non-zero. Possible applications include the construction of generalizations of Euler's dilogarithm which satisfy natural generalizations of Abel's 5-term functional equation for the dilogarithm. A graduate student will employ a computer program Hain has written to aid in investigating the dilogarithm. The program decomposes representations of symmetric groups, which arise as huge tensor products. A high-powered personal computer will be devoted to this task.