The algebraic Mandelbrot set (Laurent Bartholdi, University of Saarbrücken)

18.11.2021 13:15 – 14:15

We know since the beginnings of complex dynamics that very simple systems such as degree-2 polynomials exhibit extreme richness. They are (since the work of Douady, Hubbard, Thurston) often approached through combinatorial methods such as laminations or Hubbard trees. I will explain a more algebraic language, in which the maps are represented by group actions on rooted trees; and the relationships between the maps are encoded into natural relations between these groups. I will show how the group-theoretical language naturally relates the combinatorial invariants, and present an algebraic model of the Mandelbrot set, whose elements are groups rather than polynomials.

This is joint work with Dzmitry Dudko and Volodymyr Nekrashevych.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes et géométrie"

entrée libre