BIRATIONAL AUTOMORPHISM GROUPS AND THE MOVABLE CONE THEOREM FOR CALABI-YAU MANIFOLDS OF WEHLER TYPE VIA UNIVERSAL COXETER GROUPS

Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds X of arbitrary dimension n, for which Bir(X) is infinite and the Kawamata-Morrison movable cone conjecture is satisfied. For this family, the movable cone is explicitly described; it's fractal nature is related to limit sets of Kleinian groups and to the Apollonian Gasket. Then, we produce explicit examples of (biregular) automorphisms with positive entropy on some Calabi-Yau varieties.