Abstract Koranyi Koranyi will continue his investigations of harmonic analysis on Riemannian symmetric spaces with an emphasis on harmonic functions and relations with complex analysis. Of particular interest will be solving the long-standing problem of a local Fatou theorem for harmonic functions on symmetric spaces. This will be approached through the theory of discrete buildings. A second direction of research will be the use of quasiconformal maps in several complex variables. A primary concern here is the extension of quasiconformal maps of the boundary of a strictly pseudoconvex domain to the interior as symplectic quasiconformal maps with respect to the Bergman metric. The analysis involved in this research rests on the theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, which has beenone of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics especially quantum mechanics and elementary particle physics.
