English
Definable holomorphic continuations in o-minimal structures
Multi angle
Auteurs : Padgett, Adele (Auteur de la Conférence)
CIRM (Editeur )
03C40 - Interpolation, preservation, definability
03C64 - Model theory of ordered structures; o-minimality
32B20 - Semi-analytic sets and subanalytic sets, See also {14P15}
32D15 - Continuation of analytic objects
CIRM (Editeur )
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Résumé :
A real analytic function can always be continued holomorphically to some domain. However, the holomorphic continuations of definable functions in an o-minimal structure may not be definable. I will present joint work with P. Speissegger in which we study holomorphic continuations of functions definable in two o-minimal expansions of the real field. I will also discuss how to apply these results to the complex Gamma function and Riemann zeta function.
Keywords : o-minimality; definability; analytic continuation; multisummable series; convergent generalized power series
Codes MSC : Keywords : o-minimality; definability; analytic continuation; multisummable series; convergent generalized power series
03C40 - Interpolation, preservation, definability
03C64 - Model theory of ordered structures; o-minimality
32B20 - Semi-analytic sets and subanalytic sets, See also {14P15}
32D15 - Continuation of analytic objects
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 28/02/2025 Date de captation : 10/02/2025 Sous collection : Research talks arXiv category : Logic ; Complex Variables Domaine : Analysis and its Applications ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 00:53:57 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-02-10_Padgett.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3Organisateurs de la rencontre : Matusinski, Mickael ; Rond, Guillaume ; Servi, Tamara ; Speissegger, Patrick Dates : 10/02/2025 - 14/02/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3269.html
Données de citation
DOI : 10.24350/CIRM.V.20304103Citer cette vidéo: Padgett, Adele (2025). Definable holomorphic continuations in o-minimal structures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20304103 URI : http://dx.doi.org/10.24350/CIRM.V.20304103 |
Voir aussi
- [Multi angle] Parametrizations in valued fields / Auteur de la Conférence Vermeulen, Floris.
- [Multi angle] Sharply o-minimal structures and sharp cell decomposition / Auteur de la Conférence Zak, Benny.
- [Multi angle] Hensel minimality / Auteur de la Conférence Rideau-Kikuchi, Silvain.
- [Multi angle] Tame geometry in quantum field theory and gravity / Auteur de la Conférence Grimm, Thomas.
Bibliographie
- BIANCONI, Ricardo. Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function. The Journal of Symbolic Logic, 1997, vol. 62, no 4, p. 1173-1178. - http://doi.org/10.2307/2275634
- T. Kaiser. Global complexification of real analytic globally subanalytic functions. Israel J. Math., 213(1):139–173, 2016 - https://doi.org/10.1007/s11856-016-1306-9
- KAISER, Tobias et SPEISSEGGER, Patrick. Analytic continuations of log-exp-analytic germs. Transactions of the American Mathematical Society, 2019, vol. 371, no 7, p. 5203-5246. - https://doi.org/10.1090/tran/7748
- WILKIE, Alex J. Complex continuations of ℝan, exp-definable unary functions with a diophantine application. Journal of the London Mathematical Society, 2016, vol. 93, no 3, p. 547-566. - https://doi.org/10.1112/jlms/jdw007
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