Mathematical Sciences: Diophantine Approximations of Algebraic Points

Vojta教授将研究算术几何特别是关于变量的有理点和积分点的有限陈述。他特别想继续探索丢番图近似和奈万林纳理论之间的类比。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 Vojta will work in arithmetic geometry specifically finiteness statements for rational and integral points on varieties. In particular he wants to continue to explore insights into the analogies between diophantine approximations and Nevanlinna theory. 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.