Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von Jakob Kröker
Algorithmic construction of Hurwitz maps
Heuristic algorithms over finite fields together with number theory methods, algorithm optimization and parallelization techniques can be used to solve moderate polynomial systems and applied e.g. for complex approximation of sphere coverings:
Given a fixed set Q of branch values and k-tuple of permutations representing the monodromy of a sphere covering degree-d rational map, compute an arbitrarily precise floating-point complex approximation of that map,
(Joint project with Laurent Bartholdi and Hans-Christian v. Bothmer).
The computation was used to construct an approximation of Cui's "Sierpinsky map", a rational map whose Julia set is a Sierpinski carpet.