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The model theory of Hardy fields and linear differential equations
Multi angle
Authors : Aschenbrenner, Matthias (Author of the conference)
CIRM (Publisher )
03C64 - Model theory of ordered structures; o-minimality
12J25 - Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10}
34E05 - Asymptotic expansions
CIRM (Publisher )
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Abstract :
Hardy fields form a natural domain for a 'tame' part of asymptotic analysis. In this talk I will explain how a recent theorem which permits the transfer of statements concerning algebraic differential equations between Hardy fields and related structures yields applications to some classical linear differential equations. (Joint work with L. van den Driesand J. van der Hoeven.)
Keywords : Hardy fields; algebraic differential equations; model theory
MSC Codes : Keywords : Hardy fields; algebraic differential equations; model theory
03C64 - Model theory of ordered structures; o-minimality
12J25 - Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10}
34E05 - Asymptotic expansions
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 02/06/2023 Subseries : Research talks arXiv category : Logic ; Classical Analysis and ODEs ; Dynamical Systems Mathematical Area(s) : Algebra ; Analysis and its Applications ; Dynamical Systems & ODE ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:07:38 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_06-02_Aschenbrenner.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésEvent Organizers : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2761.html
Citation Data
DOI : 10.24350/CIRM.V.20050303Cite this video as: Aschenbrenner, Matthias (2023). The model theory of Hardy fields and linear differential equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20050303 URI : http://dx.doi.org/10.24350/CIRM.V.20050303 |
See Also
- [Multi angle] Beautiful pairs revisited / Author of the conference Ye, Jinhe.
- [Multi angle] An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case / Author of the conference Vicaria, Mariana.
- [Multi angle] Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field / Author of the conference Szachniewicz, Michal.
- [Multi angle] Interpretable, definably semisimple groups in various valued fields / Author of the conference Peterzil, Ya'acov.
- [Multi angle] The existential closedness problem for analytic solutions of difference equations / Author of the conference Padgett, Adele.
- [Multi angle] Multi topological fields and NTP2 / Author of the conference Montenegro Guzman, Samaria.
- [Multi angle] A Hasse principle over Berkovich analytic curves / Author of the conference Mehmeti, Vlerë.
- [Multi angle] Definable convex and henselian valuations on ordered fields / Author of the conference Krapp, Lothar Sebastian.
- [Multi angle] Beyond the Fontaine-Wintenberger theorem / Author of the conference Kartas, Konstantinos.
- [Multi angle] Around NIP Noetherian domains / Author of the conference Johnson, Will.
- [Multi angle] An invitation to globally valued fields / Author of the conference Hrushovski, Ehud.
- [Multi angle] Lang-Weil type bounds in finite difference fields / Author of the conference Hils, Martin.
- [Multi angle] Residue field domination / Author of the conference Haskell, Deirdre.
- [Multi angle] Motivic integration with pseudo-finite residue field and fundamental lemma / Author of the conference Forey, Arthur.
- [Multi angle] Tropical functions on skeletons / Author of the conference Ducros, Antoine.
- [Multi angle] Contracting endomorphisms of valued fields / Author of the conference Dor, Yuval.
- [Multi angle] Ax-Kochen-Ershov principles for finitely ramified henselian fields / Author of the conference Dittmann, Philip.
- [Multi angle] Group construction in $C$-minimal structures / Author of the conference Delon, Françoise.
- [Multi angle] Homology groups in algebraically closed valued fields / Author of the conference Cubides Kovacsics, Pablo.
- [Multi angle] Existential uniform p-adic integration and descent for integrability and largest poles / Author of the conference Cluckers, Raf.
- [Multi angle] Polynomials that vanish on many sets of codimension 2 / Author of the conference Ben Yaacov, Itaï.
- [Multi angle] Transfer of decidability for existential theories of (valued) fields / Author of the conference Anscombe, Sylvy.
Bibliography
- ASCHENBRENNER, Matthias, DRIES, Lou van den, et VAN DER HOEVEN, Joris. Maximal Hardy Fields. arXiv preprint arXiv:2304.10846, 2023. - https://doi.org/10.48550/arXiv.2304.10846
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