English
Introduction to Thurston's theorems
Multi angle
Auteurs : Hubbard, John H. (Auteur de la Conférence)
CIRM (Editeur )
30F40 - Kleinian groups, See also {20H10}
30F60 - Teichmüller theory
32G05 - Deformations of complex structures
37F35 - Conformal densities and Hausdorff dimension
37F45 37F40 - Geometric limits in holomorphic dynamics
CIRM (Editeur )
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Résumé :
W. Thurston's theorems almost all aim to give a purely topological problem an appropriate geometry, or to identify an appropriate obstruction.. We will illustrate this in two examples:
--The Thurston pullback map to make a rational map from a post-critically finite branched cover of the sphere, and
--The skinning lemma, to find a hyperbolic structure for a Haken 3-manifold.
In both cases, either the relevant map on Teichmüller space has a fixed point, solving the geometrization problem, or there is an obstruction consisting a multicurve.
Keywords : Teichmüller theory; Thurston pull-back map; Skinning lemma
Codes MSC : --The Thurston pullback map to make a rational map from a post-critically finite branched cover of the sphere, and
--The skinning lemma, to find a hyperbolic structure for a Haken 3-manifold.
In both cases, either the relevant map on Teichmüller space has a fixed point, solving the geometrization problem, or there is an obstruction consisting a multicurve.
Keywords : Teichmüller theory; Thurston pull-back map; Skinning lemma
30F40 - Kleinian groups, See also {20H10}
30F60 - Teichmüller theory
32G05 - Deformations of complex structures
37F35 - Conformal densities and Hausdorff dimension
37F45 37F40 - Geometric limits in holomorphic dynamics
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 02/11/2021 Date de captation : 20/09/2021 Sous collection : Research School arXiv category : Dynamical Systems ; Electrical Engineering and Systems Science Domaine : Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Durée : 00:59:25 Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-20_Hubbard.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeOrganisateurs de la rencontre : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2546.html
Données de citation
DOI : 10.24350/CIRM.V.19812603Citer cette vidéo: Hubbard, John H. (2021). Introduction to Thurston's theorems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19812603 URI : http://dx.doi.org/10.24350/CIRM.V.19812603 |
Voir aussi
- [Virtualconference] Renormalization in complex dynamics / Auteur de la Conférence Shishikura, Mitsuhiro.
- [Multi angle] Characterizing Thurston maps by lifting trees / Auteur de la Conférence Winarski, Rebecca.
- [Multi angle] Docile transcendental entire functions / Auteur de la Conférence Waterman, James.
- [Virtualconference] Characterizing rational maps positively using graphs / Auteur de la Conférence Thurston, Dylan.
- [Multi angle] Transcendental Thurston Theory for entire functions and compositions / Auteur de la Conférence Shemyakov, Sergey.
- [Multi angle] Iterated monodromy groups and transcendental dynamics / Auteur de la Conférence Reinke, Bernhard.
- [Multi angle] A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$ / Auteur de la Conférence Petersen, Carsten Lunde.
- [Virtualconference] Entire functions with Cantor bouquet Julia sets / Auteur de la Conférence Pardo-Simon, Leticia.
- [Multi angle] Contracting self-similar groups and conformal dimension / Auteur de la Conférence Nekrashevych, Volodymyr.
- [Virtualconference] Interbreeding in conformal dynamics, and its applications near and far / Auteur de la Conférence Mukherjee, Sabyasachi.
- [Multi angle] Wandering lakes of Wada / Auteur de la Conférence Martí-Pete, David.
- [Multi angle] Story of the Feigenbaum point / Auteur de la Conférence Lyubich, Mikhail.
- [Multi angle] Transcendental Julia sets of minimal Hausdorff dimension / Auteur de la Conférence Lazebnik, Kirill.
- [Multi angle] Decomposition results in rational dynamics / Auteur de la Conférence Hlushchanka, Mikhail.
- [Multi angle] Meromorphic maps of finite type: parameter space / Auteur de la Conférence Fagella, Nuria.
- [Multi angle] Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics / Auteur de la Conférence Estevez Jacinto, Gabriela Alexandra.
- [Virtualconference] Near-degenerate regime in neutral renormalization / Auteur de la Conférence Dudko, Dzmitry.
- [Multi angle] Box renormalization as a 'black box' / Auteur de la Conférence Drach, Kostiantyn.
- [Virtualconference] Arithmetic geometric models for the renormalisation of irrationally indifferent attractors / Auteur de la Conférence Cheraghi, Davoud.
- [Virtualconference] Tips of tongues in the double standard family / Auteur de la Conférence Buff, Xavier.
- [Multi angle] Eremenko's conjecture, Devaney's hairs, and the growth of counterexamples / Auteur de la Conférence Brown, Andrew.
- [Virtualconference] The visual sphere of an expanding Thurston map / Auteur de la Conférence Bonk, Mario.
- [Multi angle] Transcendental dynamics and infinite-dimensional Thurston theory / Auteur de la Conférence Bogdanov, Konstantin.
- [Virtualconference] Transcendental functions with small singular sets / Auteur de la Conférence Bishop, Christopher.
- [Multi angle] Polynomial versus transcendental dynamics / Auteur de la Conférence Benini, Anna Miriam.
- [Multi angle] Quadratic polynomials / Auteur de la Conférence Bartholdi, Laurent.
Bibliographie
- Hubbard, Teichmüller theory vols 1-4, Matrix editions -
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