Mathematical Sciences: Integral Quadratic and Hermitian Forms

该奖项支持宾夕法尼亚州立大学唐纳德·詹姆斯教授的二次型研究。詹姆斯博士的项目是研究数域的整数环上的二次型和厄米形式，特别强调分类、对角化和表示的理论。除了数数之外，数论是数学中最古老的分支，它研究的是整数的性质。在现代，数论中的问题为纯代数、分析和几何领域的新数学的创造提供了动力；数论的一些最新和最惊人的应用出现在理论计算机科学和编码理论中。二次型理论是数论的一个方面，几乎和整个数论领域本身一样古老，19世纪伟大的数学家高斯（C.F. Gauss）把它推进得特别远。即使在今天，数论的这个分支仍然保持着它的活力，并被证明在物理学和数学的许多分支中都有应用。

This award supports the research in quadratic forms of Professor Donald James of the Pennsylvania State University. Dr. James's project is to study quadratic and Hermitian forms over integer rings of number fields, with special emphasis on the theory of classification, diagonalization, and representation. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory. The theory of quadratic forms is an aspect of number theory that is almost as ancient as the whole field itself, and was advanced especially far by the great nineteenth-century mathematician C.F. Gauss. This subfield of number theory retains its vitality even today, and has proved to have applications both in physics and in many branches of mathematics.