Mathematical Sciences: Arithmetic of Motives and Shimura Varieties

布拉修斯教授将继续他对志村的研究 品种及其相关的动机。他会研究动机 使用稳定迹公式附加到Hilbert模形式 和内窥镜检查。 他还将研究这些项的mod p约化 品种 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 Blasius will continue his work on Shimura varieties and their associated motives. He will study motives attached to Hilbert modular forms using the stable trace formula and endoscopy. He will also study reductions mod p of these varieties. 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.