Objetivo Dynamical systems play an important role all over science, from celestial mechanics, evolution biology and economics to mathematics. Specifically holomorphic dynamics has been credited as “straddling the traditional borders between pure and applied mathematics”. Activities of numerous top-level mathematicians, including Fields medalists and Abel laureates, demonstrate the attractivity of holomorphic dynamics as an active and challenging research field.We propose to work on a research project based in holomorphic dynamics that actively connects to adjacent mathematical fields. We work on four closely connected Themes:A. we develop a classification of holomorphic dynamical systems and a Rigidity Principle, proposing the view that many of the additional challenges of non-polynomial rational maps are encoded in the simpler polynomial setting;B. we advance Thurston’s fundamental characterization theorem of rational maps and his lamination theory to the world of transcendental maps, developing a novel way of understanding of spaces of iterated polynomials and transcendental maps;C. we develop an extremely efficient polynomial root finder based on Newton’s method that turns the perceived problem of “chaotic dynamics” into an advantage, factorizing polynomials of degree several million in a matter of minutes rather than months – and providing a family of rational maps that are highly susceptible to combinatorial analysis, leading the way for an understanding of more general maps; D. and we connect this to geometric group theory via “Iterated Monodromy Groups”, an innovativeconcept that helps solve dynamical questions in terms of their group structure, and that contributes to geometric group theory by providing natural classes of groups with properties that used to be thought of as “exotic”. Ámbito científico social scienceseconomics and businesseconomicseconometricsnatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesphysical sciencesastronomyplanetary sciencescelestial mechanics Palabras clave MSC2010:37Fxx: complex dynamical systems Teichmüller theory root finding iterated monodromy groups Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-ADG-2015 - ERC Advanced Grant Convocatoria de propuestas ERC-2015-AdG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-ADG - Advanced Grant Institución de acogida UNIVERSITE D'AIX MARSEILLE Aportación neta de la UEn € 1 036 640,75 Dirección BOULEVARD CHARLES LIVON 58 LE PHARO 13284 Marseille Francia Ver en el mapa Región Provence-Alpes-Côte d’Azur Provence-Alpes-Côte d’Azur Bouches-du-Rhône Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 036 640,75 Beneficiarios (3) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo UNIVERSITE D'AIX MARSEILLE Francia Aportación neta de la UEn € 1 036 640,75 Dirección BOULEVARD CHARLES LIVON 58 LE PHARO 13284 Marseille Ver en el mapa Región Provence-Alpes-Côte d’Azur Provence-Alpes-Côte d’Azur Bouches-du-Rhône Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 036 640,75 CONSTRUCTOR UNIVERSITY BREMEN GGMBH Alemania Aportación neta de la UEn € 1 184 669,75 Dirección CAMPUS RING 1 28725 Bremen Ver en el mapa Región Bremen Bremen Bremen, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 184 669,75 TECHNISCHE UNIVERSITAT BERLIN La participación finalizó Alemania Aportación neta de la UEn € 91 170,50 Dirección STRASSE DES 17 JUNI 135 10623 Berlin Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 91 170,50
