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

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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.