Mathematical Sciences: Group-Theoretic Methods in Inverse Galois Theory

该奖项支持逆伽罗瓦问题的工作。 的 首席研究员将改善标准， 他最近把群实现为伽罗瓦群， 他还将寻找新的标准，并应用这些标准。 标准，以实现进一步感兴趣的群体类别， 特别是简单的群，如有理数上的伽罗瓦群， 在分圆域上 这项工作的大部分是基于使用 黎曼球面覆盖的模空间。 一个群是一个具有单一运算的代数结构。 它出现在数学的许多领域，以及，物理学和 化学. 代数中的一个主要问题是 通过识别那些可以被表示为 有理数上的伽罗瓦群。 这涉及到混合 代数、数论和代数几何。

This award supports work on the Inverse Galois problem. The principal investigator will improve the criteria for the realization of groups as Galois groups that he has recently found. He will also search for new criteria and apply these criteria to realize further interesting classes of groups, especially simple groups, as Galois groups over the rationals and over cyclotomic fields. Most of this work is based on the use of moduli spaces for covers of the Riemann sphere. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. One of the major problems in algebra is concerned with identifying those groups which can be represented as the Galois group over the rationals. This involves a blend of algebra, number theory and algebraic geometry.