Mathematical Sciences: Linear Series on Algebraic Varieties

拉扎斯菲尔德 Lazarsfeld教授将研究高维簇上线性级数的几何和代数性质。特别是他希望证明高维模拟藤田的猜想。他还希望工作的syzygies光滑表面和Sheshadri常数高维品种。 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世纪中却有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。 ***

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. ***