Mathematical Sciences: 1992 Summer Research Institute on 'Quadratic Forms and Division Algebras'

数学科学：1992年夏季研究所“二次形式和除代数”

• 批准号: 9122671
• 负责人: James Maxwell
• 金额: $ 10.88万
• 依托单位: American Mathematical Society
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9122671&HistoricalAwards=false
• 关键词: Mathematical; Sciences; 1992; Summer; Research

During the 1980's the closely related subjects of the algebraic theory of quadratic forms and the theory of finite- dimensional division algebras benefitted greatly from developments in algebraic K-theory and algebraic geometry. The topics of this conference, historically speaking, are rooted in number theory. Most of the main problems and motivation have number theoretic origins. In the first half of this century, these subjects blossomed with the development of modern algebraic number theory. The discovery of local-global principles for quadratic forms was bound up with the development of p-adic fields. Further, the classification of finite-dimensional division algebras over local and global fields was closely connected to the development of class field theory. In the past forty years, each of these subjects has declared much independence from number theory. This project will support the 1992 Summer Research Institute on Quadratic Forms and Division Algebras: Connections with Algebraic K-theory and Algebraic Geometry (the fortieth in the series) to be held from July 6 - 24, 1992 at the University of California, Santa Barbara. The primary topics of the summer institute are the closely related subjects of finite-dimensional division algebras and the algebraic theory of quadratic forms. Further progress is expected to be stimulated by holding two special lecture series, one devoted to algebraic K-theory and the other to algebraic geometry. In addition, there will be research lectures on the two principal themes, quadratic forms and division algebras. The first week of the institute will have quadratic forms emphasis, the third week will have division algebra emphasis, and the second week will emphasize both with the hope of stimulating interaction.

在20世纪80年代，二次型代数理论和有限维除法代数理论这两个密切相关的学科从代数k理论和代数几何的发展中获益匪浅。从历史上讲，这次会议的主题是植根于数论的。大多数主要问题和动机都有数论根源。在本世纪上半叶，这些学科随着现代代数数论的发展而蓬勃发展。二次型局部-整体原理的发现是与p进域的发展联系在一起的。此外，局部和全局域上有限维划分代数的分类与类场论的发展密切相关。在过去的四十年里，这些学科中的每一个都宣称从数论中独立出来。这个项目将支持于1992年7月6日至24日在加州大学圣巴巴拉分校举行的1992年夏季二次型和除法代数研究所：与代数k理论和代数几何的联系（该系列的第四十期）。暑期学院的主要课题是密切相关的有限维除法代数和二次型的代数理论。通过举办两个特别系列讲座，一个致力于代数k理论，另一个致力于代数几何，有望进一步取得进展。此外，将有两个主要主题的研究讲座，二次型和除法代数。课程的第一周将强调二次型，第三周将强调除法代数，第二周将强调两者，希望能促进互动。