Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Complex dynamics, in the sense of iteration theory of holomorphic mappings, is a very active and deep field with many connections all across mathematics, with profound recent developments and important goals. Its connections to other branches of mathematics include geometry of 3-manifolds (through Sullivan’s celebrated “dictionary” between holomorphic dynamics and Kleinian groups, as well as Thurston’s geometrization theory), algebra (in particular group theory, through Nekrashevych’ theory of Iterated Monodromy Groups), renormalization (that plays an important role in the study of holomorphic dynamics as well as in physics), all the way to numerical analysis (many equation solvers and root finders are iterated holomorphic maps). Our focus will be on selected topics of holomorphic dynamics that have seen substantial developments in the past years that open up new perspectives and vistas. We will put particular emphasis on their interconnections, helping an actively developing field to maintain coherence and a view towards “the whole picture”. One substantial ingredient of the conference is the Advanced Grant of the European Research Council “Hologram” by one of the organizers; the intended time period for the conference (September 2021) marks the conclusion of this grant, so it is a good opportunity to “pass on the torch” to the community-at-large in terms of accomplishments and questions achieved. We hope that the results of this grant will inspire our colleagues to apply for other major grants, ERC and other wise.
