U.S.-U.K. Collaborative Research: Exponentiation and O-Minimal Expansions of R

9224546标记 这三年的美国奖-英国数学合作研究涉及大卫E。马克角伊利诺伊大学芝加哥校区和厄巴纳-香槟校区的沃德·亨森、卢·货车登·德里斯，以及牛津大学数学研究所的安格斯·麦金太尔、亚历克斯·威尔基和科比·彼得齐尔。 研究的目的是将复分析方法应用于R的指数和O-极小展开的模型理论。 模型的理论结果表明，如此公平的R可定义指数子集的行为在许多方面像半代数和子解析子集。 研究人员将研究R的更精细的可定义性和增长率问题，并将其结果扩展到自然扩展，从而进一步分析结构。 这项合作利用了牛津大学和伊利诺伊大学研究小组的互补专业知识。 两人都在模型理论和分析界面、指数运算和指数项定义的复函数研究方面有着广泛的工作。 由于指数定义的半代数和子解析集自然出现在许多数学和工程领域，这项研究将促进他们的使用在真实的代数和真实的解析几何，动力系统，控制理论，统计和机器人的理解。 ***

9224546 Marker This three-year award for U.S.-United Kingdom cooperative research in mathematics involves David E. Marker, C. Ward Henson, Lou van den Dries of the Chicago and Urbana-Champaign campuses of the University of Illinois respectively, and Angus Macintyre, Alex Wilkie, Kobi Peterzil of Oxford University's Mathematics Institute. The objectives of the research is to apply complex analytical methods to model theory in exponentiation and O- minimal expansions of R. Model theoretical results obtained so fair show that subsets of R definable exponentiation behave in many ways like semialgebraic and subanalytic subsets. The investigators will study finer definability and growth rate questions of R and extend their results to natural expansions allowing further analytical structure. This collaboration takes advantage of the complementary expertise of the Oxford and University of Illinois research groups. Both have worked extensively on model theory and analysis interface, exponentiation, and study of complex function defined in exponential terms. Since exponentially defined semialgebraic and subanalytic sets arise naturally in many mathematical and engineering fields, this research will advance understanding of their uses in real algebraic and real analytic geometry, dynamical systems, control theory, statistics and robotics. ***