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

9224546马克这个为期三年的美英数学合作研究奖的获得者包括分别来自伊利诺伊大学芝加哥分校和厄巴纳-香槟分校的大卫·e·马克、c·沃德·汉森、卢·范登·德雷斯，以及牛津大学数学研究所的安格斯·麦金泰尔、亚历克斯·威尔基、科比·彼得齐尔。本研究的目的是将复解析方法应用于R的幂次和O-极小展开式的模型理论中，得到的模型理论结果表明，R可定义幂次的子集在许多方面具有半代数子集和亚解析子集的性质。研究人员将研究R的更精细的可定义性和增长率问题，并将其结果扩展到允许进一步分析结构的自然展开。此次合作充分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。他们在模型理论和分析界面、指数化以及用指数定义的复函数的研究方面做了大量的工作。由于指数定义的半代数和亚解析集在许多数学和工程领域自然出现，本研究将促进对它们在真实代数和真实解析几何、动力系统、控制理论、统计学和机器人中的应用的理解。＊＊＊

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. ***