Mathematical Sciences: Nonvanishing L2-Cohomology of Arithmetic Varieties

该奖项支持普渡大学John S.P. Wang教授对李群表示的研究。Wang博士的课题是研究半单连通李群的Zuckerman模与群的商的L2上同调之间的一个猜想。王教授早期的工作已经在许多情况下证明了这个猜想的正确性，他的结果不仅在李群的一般理论中具有重要意义，而且在更特殊的自同构函数领域中也具有重要意义。群论开始于19世纪早期，它描述了可以连续完成的操作，也可以撤销，就像90度的顺时针旋转被90度的逆时针旋转撤销一样。李群是在19世纪后期由开创性的挪威数学家索菲斯·李发展起来的，他对微分方程的最基本问题很感兴趣。一百年后的今天，群论渗透到现代数学中，李群在数学的许多分支和物理学中的应用也丝毫未减。

This award supports the research in the representations of Lie groups by Professor John S.P. Wang of Purdue University. Dr. Wang's project is to work on a conjecture relating Zuckerman modules of a semisimple connected Lie group to the L2 cohomology of the quotient of the group by a well-chosen discrete subgroup. Professor Wang's earlier work has already provided evidence of the truth of this conjecture in many cases, and his results will be of importance not only in the general theory of Lie Groups but also in the more special field of automorphic functions. Group theory began in the early nineteenth century as a description of operations that might be done successively, and also undone, as a ninety-degree clockwise rotation is undone by the ninety-degree counterclockwise rotation. Lie groups were developed in the late part of that century by the path breaking Norwegian mathematician Sophus Lie, who was interested in the most fundamental questions concerning differential equations. Now, one hundred years later, group theory pervades modern mathematics, and the utility of Lie groups in many branches of mathematics, as well as in physics, has continued undiminished.