Absolute Galois groups and Massey products

大约200年前，E。伽罗瓦发现了一个绝妙的想法，将对称性作为一个对象来研究，并以这种方式解决与给定数学结构相关的基本和看似棘手的问题。今天伽罗瓦理论是现代数学的核心部分，也在物理学和化学的某些部分中找到。然而，伽罗瓦理论中的一些基本问题仍然是开放的。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，有许多集合体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，我们就有可能解决一些解方程的基本问题，代数和几何，拓扑，物理，密码学的进一步问题;以及大型数据系统的问题。

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.