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

国际研究奖学金项目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。该计划的奖励为联合研究提供了机会，并利用独特或互补的设施、专业知识和国外的实验条件。该奖项将支持Joshua wisconsin博士和Katrin Tent博士在德国Universität mnster进行为期24个月的研究。群是一种数学结构，它为物体的对称性集合建模。有限Morley秩的群构成了数理逻辑中自然产生的一类群，这些群具有一个称为Morley秩的维数概念。本文提出了对某对象具有多重传递作用的有限Morley秩单群的分类，从而进一步推动了目前对所有有限Morley秩单群的分类。此外，本文还研究了一类更一般的有限Morley秩的一般乘传递群。重点是建立作用于一组固定Morley秩的群的一般多重传递度的自然界，并充分理解达到该界时的作用。由于对称性在纯数学以及从分子结构和量子力学到M. C.埃舍尔的艺术等主题中大量存在，因此群理论意义深远。有限Morley秩群理论与数学的许多领域紧密相关，包括数理逻辑、代数几何和数论。具体地说，有限Morley秩的简单群的分类的进展直接应用于模型理论，而有限Morley秩的一般乘法传递群的研究涉及某些经典矩阵群作用的开放问题。

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.