Mathematical Sciences: Deformations, Hodge Theory, and LP Cohomology

扎克教授将致力于研究局部对称空间以及代数几何中的超越方法。他还将研究关于纤维空间的Torelli类型问题。卡皮什潘教授将从形变理论的角度，使用微分李代数来研究霍奇理论。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。

Professor Zucker will work on locally symmetric spaces as well as transcendental methods in algebraic geometry. He will also study Torelli type questions for fibre spaces. Professor Karpishpan will work on Hodge theory from the point of view of deformation theory, using differential Lie algebras. 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.