Abelian Varieties and Their Subvarieties

Debarre教授将研究阿贝尔变体的几何性质。特别地，他将研究小次阿贝尔变换的复盖的拓扑和几何。他还打算继续研究肖特基问题。这是代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

Professor Debarre will investigate geometric properties of abelian varieties. In particular, he will study the topology and geometry of covers of abelian varieties of small degree. He also intends to continue his study of the Schottky problem. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.