Mathematical Sciences: Grothendieck Riemann-Roch on the Level of Forms

童教授将研究与广义Riemann-Roch定理有关的几个问题。他将研究Beilinson和Scheck tman在更高维度上的迹代数的推广。希望得到行列式丛上的自然联系，从而在形式的水平上给出Grothendieck Riemann Roch公式。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 Tong will work on several problems connected with generalized Riemann-Roch Theorems. He will study generalizations of the trace algebra of Beilinson and Schectman in higher dimensions. The hope is to get a natural connection on determinant bundles to give Grothendieck Riemann Roch formulas on the level of forms. 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.