Mathematical Sciences: Nonvanishing L2-Cohomology of Arithmetic Varieties

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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.