The principal investigator will continue his research in geometry and dynamical systems. One of the main parts of the research will extend verification of the Feigenbaum universality conjecture to all real exponent singularities. He will also continue to develop the Chern-Weil theory for measurable conformal structures. A third project involves a lamination theory for Riemann surfaces which may lead to a universal Teichmuller theory modeled on Hilbert space. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.
