English
Poincaré-Reeb graphs of real algebraic domains
Multi angle
Auteurs : Sorea, Miruna-Stefana (Auteur de la Conférence)
CIRM (Editeur )
14P25 - Topology of real algebraic varieties
26Cxx - Polynomials, rational functions
58K05 - Critical points of functions and mappings
05E14 - Combinatorial aspects of algebraic geometry
CIRM (Editeur )
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Résumé :
A real algebraic domain is a closed topological subsurface of a real affine plane such that its boundary consists of disjoint smooth connected components of real algebraic plane curves. Our goal is to study the nonconvexity of real algebraic domains relative to the vertical direction. To this end, we collapse all vertical segments contained in the algebraic domain, yielding a Poincar´e–Reeb graph which is naturally transversal to the foliation by vertical lines. Our main result is the following: any transversal graph whose vertices have only valencies 1 and 3 and are situated on distinct vertical lines arises up to isomorphism as a Poincar´e–Reeb graph of a real algebraic domain. We also give a purely topological description of the setting in which our construction of Poincar´e–Reeb graphs may be applied, with no differentiability assumptions. This is a joint work with Arnaud Bodin and Patrick Popescu-Pampu (Université de Lille, France).
Keywords : combinatorial type; Morse theory; Poincaré–Reeb graph; real algebraic curve; real polynomial functions
Codes MSC : Keywords : combinatorial type; Morse theory; Poincaré–Reeb graph; real algebraic curve; real polynomial functions
14P25 - Topology of real algebraic varieties
26Cxx - Polynomials, rational functions
58K05 - Critical points of functions and mappings
05E14 - Combinatorial aspects of algebraic geometry
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/11/2022 Date de captation : 25/10/2022 Sous collection : Research talks arXiv category : Group Theory Domaine : Topology Format : MP4 (.mp4) - HD Durée : 00:58:34 Audience : Researchers Download : https://videos.cirm-math.fr/2022-10-25_Sorea.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Real Algebraic Geometry / Géometrie algébrique réelleOrganisateurs de la rencontre : Bihan, Frédéric ; Brugallé, Erwan ; Dickenstein, Alicia ; Dutertre, Nicolas Dates : 24/10/2022 - 28/10/2022 Année de la rencontre : 2022 URL Congrès : https://conferences.cirm-math.fr/2626.html
Données de citation
DOI : 10.24350/CIRM.V.19978103Citer cette vidéo: Sorea, Miruna-Stefana (2022). Poincaré-Reeb graphs of real algebraic domains. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19978103 URI : http://dx.doi.org/10.24350/CIRM.V.19978103 |
Voir aussi
- [Multi angle] Random algebraic geometry - lecture 4 / Auteur de la Conférence Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 3 / Auteur de la Conférence Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 2 / Auteur de la Conférence Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 1 / Auteur de la Conférence Lerario, Antonio.
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