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

小行星9810299 国际研究员奖励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。 该计划的奖项提供了联合研究的机会，以及使用国外独特或互补的设施，专业知识和实验条件。 该奖项将支持博士约翰R。Swallow博士在以色列海法的以色列理工学院与Jack Sonn博士一起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，1）实现组作为伽罗瓦组和2）确定二次形式的等价性超过数域，使用下降理论连接二次形式理论与障碍中心伽罗瓦嵌入问题。 这项工作的一个可能的结果将是实现某些未知的2-群。 这将提供之间的联系逆伽罗瓦问题和理论的四元数代数和二次形式。 Sonn博士是中心嵌入问题理论的主要专家。 ***

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. ***