The principal investigator will study circle packings and quasiconformal mappings. One main problem to be studied is the Koeba uniformization conjecture which states that any domain in the extended complex plane is conformally homeomorphic to a circle domain in the extended plane. The techniques to be used in this study are closely related to the theory of quasiconformal maps. 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.
