International Research Fellow Awards: Descent of Quaternion Algebras and Applications to Galois Theory

9810299吞下国际研究员奖计划使美国科学家和工程师能够在国外进行三到二十四个月的研究。该项目的奖项提供了联合研究的机会，并提供了使用国外独特或互补的设施、专业知识和实验条件的机会。该奖项将支持戴维森学院的John R.Swallow博士为期12个月的博士后研究访问，与以色列海法Technion-以色列理工学院的Jack Sonn博士合作，研究四元数代数的下降和伽罗瓦理论的应用。他们将开发新的、主要是建设性的技术，用于1)将群实现为Galois群，以及2)确定数域上二次形式的等价性，使用将二次形式理论与中心Galois嵌入问题的障碍联系起来的下降理论。这项工作的可能结果之一将是实现某些未知的2-基团。这将提供伽罗瓦逆问题和四元数代数和二次型理论之间的联系。桑恩博士是中央嵌入问题理论方面的顶尖专家。***

9810299 Swallow The International Research Fellow Awards Program enables U.S. scientists and engineers to conduct three to twentyfour months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. John R. Swallow of Davidson College to work with Dr. Jack Sonn at Technion-Israel Institute of Technology in Haifa, Israel on the descent of quaternion algebras and applications to Galois Theory. They will develop new, primarily constructive techniques for 1) the realization of groups as Galois groups and 2) the determination of the equivalence of quadratic forms over number fields, using a theory of descent connecting quadratic form theory with obstructions to central Galois embedding problems. One of the likely outcomes of this work will be the realization of certain 2-groups that are not known to occur. This will provide connections between the Inverse Galois Problem and the theory of quaternionic algebras and quadratic forms. Dr. Sonn is the leading expert in the theory of central embedding problems. ***