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. ***
