Computation and visualization of general Riemann surfaces w[z] of arbitrary algebraic
functions
Date: July 20th (Saturday)
Time: 11:10-11:40
Abstract
A polynomial $p(w,z)$ in two variables $w$ and $z$ with numeric coefficients
represents an analytic function $w(z)$. As such it represents a Riemann
surface. Here we are interested in the visualization of this Riemann surface
(not only in the topological sense of determining the genus). $\Re(w(z))$ and
$\Im(w(z))$ are proper representations of the surface.
Two methods, one based on implicitization and one based on the numerical
solution of differential equations on the various sheets for the construction
of proper representations of the Riemann surface are discussed.
3D graphics of examples of various total degree are shown.
