Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

博戈莫洛夫9801591 首席研究员打算继续他的工作几何代数品种，结构的伽罗瓦集团，以及相关问题的双理性几何。他计划工作的最小优势类代数品种，渐近公式上同调的线丛，描述基本群体和普遍覆盖的代数和辛流形，以及结构复杂的辛和hyperkahler流形。他还建议工作的结构西洛子群的伽罗瓦集团和有效版本的稳定程序组上同调。 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。

Bogomolov 9801591 The principal investigator intends to continue his work on the geometry of algebraic varieties, the structure of Galois groups, and related problems in birational geometry. He plans to work on constructing minimal dominant classes of algebraic varieties, asymptotic formulas for cohomology of line bundles, the description of fundamental groups and universal coverings of algebraic and symplectic manifolds, and the structure of complex symplectic and hyperkahler manifolds. He also proposes to work on the structure of Sylow subgroups of the Galois groups and on the effective version of the stabilization procedure for group cohomology. 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.