Mathematical Sciences: Kloosterman Sums and Traces of Lisse Sheaves as Algebraic Integers

Fisher教授会讲Kloosterman和的等分布定理。他还希望将卡茨的等分布定理推广到数域中带迹的lisse束。他还希望从数值上研究Kloosterman和的特殊性。这个项目属于算术几何的一般领域，它融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。

Professor Fisher will work on the equidistribution theorem for Kloosterman sums. He also hopes to generalize Katz's equidistribution theorem to lisse sheaves with traces in a number field. He also hopes to study numerically the distinctness of Kloosterman sums. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.