Mathematical Sciences: Linear Series on Algebraic Varieties

Lazarsfeld教授将研究高维簇上线性级数的几何和代数性质。特别是，他希望证明藤田猜想的高维类比。他还希望研究光滑表面的合子和高维变种上的Sheshadri常数。这是在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25年里，它已经取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。***

Lazarsfeld Professor Lazarsfeld will investigate geometric and algebraic properties of linear series on higher dimensional varieties. In particular he hopes to prove the higher dimensional analogue of Fujita's conjecture. He also hopes to work on syzygies of smooth surfaces and Sheshadri constants on higher dimensional varieties. 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. ***