Mathematical Sciences: Quadratic Forms and Galois Cohomology

在二次型理论的现代发展中，寻找不变量一直是最重要的问题之一。在Witt环的语言中，这是一个寻找从Witt环的各个部分或子商到其他代数实体的同态的问题，希望更容易管理。这个项目研究了这个问题的一个重要的子问题的几个方面，称为Arason-Milnor问题。这项研究涉及二次型理论，它研究齐次二次多项式的解，或者等价地，研究具有对称内积的空间的几何。概述的项目涉及代数二次型领域中的一些最重要的问题。

In the modern development of quadratic form theory, one of the most important problems has always been that of finding invariants. In the language of Witt rings, this is the problem of finding homomorphisms from various parts or subquotients of the Witt ring into other, hopefully more manageable, algebraic entities. This project studies several aspects of an important subproblem of this problem called the Arason-Milnor problem. This research concerns the theory of quadratic forms which is a study of the solutions of homogeneous second degree polynomials, or equivalently, the study of the geometry of spaces possessing a symmetric inner product. The project outlined concerns some of the most important problems in the area of algebraic quadratic forms.