Absolute Galois groups and Massey products

绝对伽罗瓦群和梅西积

• 批准号: RGPIN-2017-05344
• 负责人: Minac, Jan
• 金额: $ 2.19万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635448
• 关键词: Absolute; Galois; groups; Massey; products

Almost 200 years ago, E. Galois discovered a brilliant idea to study symmetries as one object, and in this way to solve fundamental and seemingly intractable problems related to given mathematical structures. Today Galois theory is a central part of current mathematics, and is also found in some parts of physics and chemistry. However some basic problems in Galois theory are still open. There are many different symmetries of polynomial equations. It is a daunting task to study them. Yet there are assemblies of many of them which are known as absolute Galois groups, which gives us hope to find a pattern. If we could find the structures and basic properties of absolute Galois groups, we could possibly solve a number of fundamental problems of solving equations, further problems in algebra and geometry, topology, physics, cryptography; and problems with large data systems.

大约 200 年前，E. Galois 发现了一个绝妙的想法，将对称性作为一个对象进行研究，并以此方式解决与给定数学结构相关的基本且看似棘手的问题。今天，伽罗瓦理论是当前数学的核心部分，并且也存在于物理和化学的某些部分中。然而，伽罗瓦理论中的一些基本问题仍然悬而未决。多项式方程有许多不同的对称性。研究它们是一项艰巨的任务。然而，其中许多集合被称为绝对伽罗瓦群，这给了我们找到模式的希望。如果我们能找到绝对伽罗瓦群的结构和基本性质，我们就有可能解决许多求解方程的基本问题，以及代数和几何、拓扑、物理学、密码学中的进一步问题；以及大数据系统的问题。