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

童教授将研究与以下方面有关的几个问题： 广义Riemann-Roch定理 他将学习归纳法 Beilinson和Schectman的迹代数在高等代数中的 尺寸. 希望能和你的家人 行列式丛给出Grothendieck Riemann Roch公式 形式的水平。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。

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.