Dia: Dimecres 18 de març de 2026
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Mikhail Hlushchanka, University of Amsterdam
Títol: Quasi-visual approximations, tile graphs, and semi-hyperbolic maps
Resum: The topology and geometry of some (fractal) metric spaces can often be described by a sequence of increasingly finer covers. Each such cover provides a coarse picture of the space at increasing resolution. A quasi-visual approximation is a special sequence of covers of the space that satisfies certain natural conditions (concerning relative distances and diameters of the elements of the covers).
Quasi-visual approximations provide a convenient framework for addressing questions in quasiconformal geometry. In particular, quasi-visual approximations can be used to detect whether a given homeomorphism between two bounded metric spaces is a quasisymmetry. They are also naturally connected to the theory of Gromov hyperbolic spaces via the tile graph construction. In a dynamical setting, a sequence of covers of the underlying space may be produced naturally by starting with an initial cover and then pulling it back by the iterates of the map. We show that for rational maps such a dynamical sequence of covers of the Julia set is quasi-visual if and only if the map is semi-hyperbolic. (Based on joint work with Mario Bonk and Daniel Meyer)Last updated: Sun Mar 15 10:10:58 2026