Mathematical Sciences: Topics in Iwasawa Theory

琼斯教授将研究椭圆曲线的岩川理论。他打算研究与L-进表示的Iwasawa L-函数有关的问题。他还将研究等变上同调，以期找到平对偶定理的类似物。这个项目属于算术几何的一般领域，这门学科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 Jones will work on the Iwasawa theory of elliptic curves. He intends to study problems related to Iwasawa L- functions of l-adic representations. He will also study equivariant cohomology with a view towards finding analogues of flat duality theorems. 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.