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IRFP: Multiply transitive and generically multiply transitive groups of finite Morley rank

IRFP：有限莫利秩的乘法传递群和一般乘法传递群

基本信息

批准号：
1064446
负责人：
Joshua Wiscons
金额：
$ 13.21万
依托单位：
Wiscons Josh
依托单位国家：
美国
项目类别：
Fellowship Award
财政年份：
2012
资助国家：
美国
起止时间：
2012-07-01 至 2014-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1064446&HistoricalAwards=false
关键词：
IRFP Multiply transitive generically multiply

项目摘要

The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four 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 twenty-four-month research fellowship by Dr. Joshua Wiscons to work with Prof. Dr. Dr. Katrin Tent at the Universität Münster in Germany.Groups are mathematical structures that model collections of symmetries of objects. The groups of finite Morley rank form a class of groups, naturally arising in mathematical logic, which are equipped with a notion of dimension called Morley rank. This project advances the classification of the simple groups of finite Morley rank that have a multiply transitive action on some object and, consequently, furthers the current effort to classify all simple groups of finite Morley rank. Additionally, this project investigates the more general class of generically multiply transitive groups of finite Morley rank. The focus is on establishing a natural bound on the degree of generic multiple transitivity for groups acting on a set of fixed Morley rank and to fully understand the action in the case when the bound is achieved.As symmetries abound in pure mathematics as well as in topics ranging from the structure of molecules and quantum mechanics to the art of M. C. Escher, the theory of groups is far-reaching. The theory of groups of finite Morley rank is tied up with many areas of mathematics including mathematical logic, algebraic geometry, and number theory. Specifically, progress on the classification of the simple groups of finite Morley rank has direct applications to model theory, while the investigation of generically multiply transitive groups of finite Morley rank touches on open problems regarding actions of certain classical matrix groups.

国际研究奖学金计划使美国科学家和工程师能够在国外进行9至24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。该奖项将支持约书亚Wiscons博士与Katrin Tent博士教授在德国明斯特大学进行为期24个月的研究。群是对对象的对称性集合进行建模的数学结构。有限莫利秩的群形成了一类群，自然地出现在数理逻辑中，它们配备了称为莫利秩的维数概念。这个项目推进了有限莫利秩的单群的分类，这些单群对某些对象具有多重传递作用，因此，进一步推进了目前对有限莫利秩的单群进行分类的努力。此外，本计画研究有限莫利秩的一般多重传递群的更一般的类。本文的重点是建立作用于固定莫利秩集合上的群的通有多重传递性的一个自然界，并充分理解当达到这个界时的作用。C.因此，群论的影响是深远的。有限莫利秩群的理论与数学的许多领域联系在一起，包括数理逻辑、代数几何和数论。具体来说，进展分类的简单群体的有限莫利秩有直接的应用模型理论，而调查一般多传递群体的有限莫利秩触及开放的问题，有关行动的某些经典矩阵群。