Mathematical Sciences: Intersection Theory and P-adic Dynamical Systems

基廷9500982基廷教授将致力于算术几何的问题。他将尝试计算交换簇的模空间上某些因子的算术交数。他还将从范数领域的角度研究p-进动力系统的一般理论。最后，他希望研究形式群的某些自同构群在该群的变形模空间上的作用。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。

Keating 9500982 Professor Keating will work on problems in arithmetic geometry. He will try to compute the arithmetical intersection numbers for certain divisors on moduli spaces of abelian varieties. He also will study the general theory of p-adic dynamical systems from he point of view of the field of norms. Finally he wishes to study the actions of certain automorphism groups of formal groups on the moduli space of deformations of that group. 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.