# Laurent Bartholdi: Insanely twisted rabbits

Laurent Bartholdi, Georg-August University of Göttingen, Germany

**Time: **Wed 2009-11-18 16.00

**Location: **Room 3721, department of mathematics, KTH, Lindstedtsvägen 25, 7th floor

(Topological) branched coverings of the sphere, modulo a natural ("isotopy") relation, are interesting combinatorial objects; and a result by Thurston explains, at least theoretically, when such a covering is equivalent to a rational map. I will explain how such coverings can be conveniently encoded in group theory, and how that language can be used to answer a long-standing open problem by Douady and Hubbard, the "Twisted rabbit problem". I will then discuss visualizations of "matings" of polynomials (the topological branched covering obtained from gluing together two polynomials at infinity) through the same method. This is joint work with Volodya Nekrashevych.

Coffee and tea is served at 3:30 in the lunch room.