Office: 4-112 Mathematics Building
Dept. Phone: (631)-632-8290
Time and place: MWF 11:45am-12:40pm Physics P122
Every simply connected planar domain (except the plane itself) can be mapped by a 1-1, onto holomorphic function to the disk. This is the Riemann mapping theorem, and in this course we will discuss the result from many points of view including such topics as boundary behavior, computational algorithms, generalizations to quasiconformal mappings, hyperbolic geometry, multiply connected domains. Of particular interest are connections with computational geometry.
The prerequisites are a first course in complex analysis, although I will attempt to be as self contained as is reasonable. In general, we will try to touch on a wide variety of topics, sometimes merely stating results without proof. In addition to the topics listed above, we will also deal briefly with things like Gauss quadrature, numerical linear algebra, the fast Fourier transform, the multipole method.
The notes so far, Oct 2009
A fast mapping theorem for polygons
Howell's thesis discussion of divergence in Davis method starts on page 62.