Mathematical Sciences: Quadratic Forms and Galois Cohomology

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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.