Mathematical Sciences: Diophantine Geometry and Differential Algebraic Geometry

9500331布伊姆教授将致力于算术几何，特别是丢番图几何中的问题。他将使用微分代数几何的技巧来研究朗氏猜想、马祖尔猜想的半阿贝尔情形以及ABC猜想与对数Kodaira维度之间的关系。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。布伊姆教授的研究甚至包括了一个来自经典分析的成分。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。

9500331 Buium Professor Buium will work in arithmetic geometry specifically problems in Diophantine geometry. He will use techniques from differential algebraic geometry to study Lang's conjecture, the semi-abelian case of Mazur's conjecture as well as relationships between the abc conjecture and logarithmic Kodaira dimension. 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. Professor Buium's research even includes a component coming from classical analysis. 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.