Advancing Bridges in Complex Dynamics
Avancer les connections dans la dynamique complexe
20 – 24 September 2021
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Scientific Committee
Comité scientifique Nuria Fagella (University of Barcelona) |
Organizing Committee
Comité d’organisation Anna Miriam Benini (University of Parma) |
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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. |
La dynamique complexe, au sens de la théorie itérative des applications holomorphes, est un domaine très actif et profond qui entretient de nombreuses connexions, essentiellement mathématiques, et qui compte de récents développements spectaculaires et des objectifs fondamentaux. Ses liens avec d’autres branches des mathématiques comprennent la géométrie des variétés de dimension trois (via le célèbre “dictionnaire” de Sullivan entre la dynamique holomorphe et les groupes kleinéens et via la géométrisation de Thurston), l’algèbre (en particulier la théorie géométrique des groupes, et plus particulièrement la théorie de Nekrashevych sur les groupes de monodromie itérée), la renormalisation (qui joue un rôle important dans l’ étude de la dynamique holomorphe ainsi qu’en physique), allant jusqu’à l’analyse numérique (de nombreux solveurs d’équations et recherches de racines utilisent des applications holomorphes itérées).
Nous nous concentrerons sur des sujets soigneusement choisis de la dynamique holomorphe qui ont connu des développements substantiels au cours de ces dernières années et qui ouvrent de nouvelles perspectives ainsi que des points de vue originaux. Nous mettrons particulèrement l’accent sur leurs interactions, afin de s’assurer que ces domaines en plein essor maintiennent la cohérence nécessaire à une vision globale du sujet. Un ingrédient important de la conférence est la bourse “European Research Council (ERC) Advanced Grant” Hologram détenue par l’un des organisateurs car la période prévue pour la conférence —septembre2021— marque la fin de cette subvention : c’est donc là une bonne occasion de “passer le flambeau” à la communauté en dressant le bilan des accomplissements réalisés et en posant les questions qui en sont issues. Nous espérons que les résultats obtenus grâce à cette bourse inspireront nos collègue à candidater sur d’autres bourses de cette ampleur, ERC et/ou autres. |
Xavier Buff (Université Paul Sabatier) Tips of tongues in the double standard family
Davoud Cheraghi (Imperial College London) Arithmetic geometric models for the renormalisation of irrationally indifferent attractors
Nuria Fagella (University of Barcelona) Meromorphic maps of finite type: parameter space
Mikhail Lyubich (Stony Brook University) Story of the Feigenbaum point
John Milnor (Stony Brook University) Real quadratic rational maps
Sabyasachi Mukherjee (Tata Institute of Fundamental Research) Interbreeding in conformal dynamics, and its applications near and far
Volodymyr Nekrashevych (Texas A&M University) Contracting self-similar groups and conformal dimension
Carsten Petersen (Roskilde University) A dynamical homeomorphism between the Mandelbrot set M and the parabolic Mandelbrot set M_1
Pascale Roesch (Université Paul Sabatier) Walk in some parameter space
Gwyneth Stallard (Open University) Relationships between orbits of interior and boundary points of wandering domains
Konstantin Bogdanov (Aix-Marseille Université) Transcendental dynamics and infinite-dimensional Thurston theory
Andrew Brown (University of Liverpool) Eremenko’s Conjecture, Devaney’s Hairs, and the Growth of Counterexamples
Roman Chernov (Aix-Marseille Université) On the core entropy for cosine family
Caroline Davis (Indiana University) Elastic matings
Gabriela Alexandra Estevez Jacinto (Universidade Federal Fluminense) Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics
Alex Kapiamba (University of Michigan) A strong Yoccoz inequality
Kirill Lazebnik (University of Toronto) Transcendental Julia sets of minimal Hausdorff dimension
David Marti-Pete (University of Liverpool) Wandering lakes of Wada
Hongming Nie (Pontificia Universidad Católica de Chile) Boundedness of hyperbolic components for Newton maps
Yusheng Luo (Stony Brook University) The boundaries of the main hyperbolic component
Leticia Pardo-Simon (Institute of Mathematics of the Polish Academy of Sciences) Entire functions with Cantor bouquet Julia sets
Insung Park (Indiana University Bloomington) Julia sets with Ahlfors regular conformal dimension one
Bernhard Reinke (Aix-Marseille Université) Iterated monodromy groups and transcendental dynamics
Sergey Shemyakov (Aix-Marseille Université) Transcendental Thurston Theory for entire functions and compositions
James Waterman (Stony Brook University) Docile entire functions
Kostiantyn Drach (Aix-Marseille Université) Box renormalization as a « black box »
Dzmitry Dudko (Stony Brook University) Near-degenerate regime in neutral renormalization
Mitsuhiro Shishikura (Kyoto University) Renormalization in Complex Dynamics
Transcendental dynamics:
Anna Miriam Benini (University of Parma) Transcendental dynamics part I
Christopher Bishop (Stony Brook University) Transcendental functions with small singular sets
Lasse Rempe (University of Liverpool) Dynamics in the Speiser class
John Hubbard (Cornell University) Introduction to Thurston’s theorems
Dylan Thurston (Indiana University Bloomington) Characterizing rational maps positively using graphs
Becca Winarski (College of the Holy Cross) Characterizing Thurston maps by lifting trees
Global dynamics:
Laurent Bartholdi (Georg-August University of Göttingen) Quadratic polynomials (mini-course Global dynamics)
Mario Bonk (University of California, Los Angeles) The visual sphere of an expanding Thurston map
Mikhail Hlushchanka (Aix-Marseille Université/Utrecht University)
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