English
The existential closedness problem for analytic solutions of difference equations
Multi angle
Auteurs : Padgett, Adele (Auteur de la Conférence)
CIRM (Editeur )
03C05 - Equational classes, universal algebra, See also {08Axx}
11U09 - Model theory, See also {03Cxx}
30C15 - "Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral), {For algebraic theory, See 12D10; for real methods, See 26C10}"
32A60 - Zero sets of holomorphic functions
33B15 - Gamma, beta and polygamma functions
CIRM (Editeur )
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Résumé :
The existential closedness problem for a function $f$ is to show that a system of complex polynomials in $2 n$ variables always has solutions in the graph of $f$, except when there is some geometric obstruction. Special cases have be proven for exp, Weierstrass $\wp$ functions, the Klein $j$ function, and other important functions in arithmetic geometry using a variety of techniques. Recently, some special cases have also been studied for well-known solutions of difference equations using different methods. There is potential to expand on these results by adapting the strategies used to prove existential closedness results for functions in arithmetic geometry to work for analytic solutions of difference equations.
Keywords : existential closedness; $\Gamma $-function
Codes MSC : Keywords : existential closedness; $\Gamma $-function
03C05 - Equational classes, universal algebra, See also {08Axx}
11U09 - Model theory, See also {03Cxx}
30C15 - "Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral), {For algebraic theory, See 12D10; for real methods, See 26C10}"
32A60 - Zero sets of holomorphic functions
33B15 - Gamma, beta and polygamma functions
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 23/06/2023 Date de captation : 02/06/2023 Sous collection : Research talks arXiv category : Logic Domaine : Algebraic & Complex Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 01:00:14 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_06-02_Padgett_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Model theory of valued fields / Théorie des modèles des corps valuésOrganisateurs de la rencontre : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2761.html
Données de citation
DOI : 10.24350/CIRM.V.20053103Citer cette vidéo: Padgett, Adele (2023). The existential closedness problem for analytic solutions of difference equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053103 URI : http://dx.doi.org/10.24350/CIRM.V.20053103 |
Voir aussi
- [Multi angle] Beautiful pairs revisited / Auteur de la Conférence Ye, Jinhe.
- [Multi angle] An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case / Auteur de la Conférence Vicaria, Mariana.
- [Multi angle] Existential closedness of $\mathbb{Q}^{alg}$ as a globally valued field / Auteur de la Conférence Szachniewicz, Michal.
- [Multi angle] Interpretable, definably semisimple groups in various valued fields / Auteur de la Conférence Peterzil, Ya'acov.
- [Multi angle] Multi topological fields and NTP2 / Auteur de la Conférence Montenegro Guzman, Samaria.
- [Multi angle] A Hasse principle over Berkovich analytic curves / Auteur de la Conférence Mehmeti, Vlerë.
- [Multi angle] Definable convex and henselian valuations on ordered fields / Auteur de la Conférence Krapp, Lothar Sebastian.
- [Multi angle] Beyond the Fontaine-Wintenberger theorem / Auteur de la Conférence Kartas, Konstantinos.
- [Multi angle] Around NIP Noetherian domains / Auteur de la Conférence Johnson, Will.
- [Multi angle] An invitation to globally valued fields / Auteur de la Conférence Hrushovski, Ehud.
- [Multi angle] Lang-Weil type bounds in finite difference fields / Auteur de la Conférence Hils, Martin.
- [Multi angle] Residue field domination / Auteur de la Conférence Haskell, Deirdre.
- [Multi angle] Motivic integration with pseudo-finite residue field and fundamental lemma / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Tropical functions on skeletons / Auteur de la Conférence Ducros, Antoine.
- [Multi angle] Contracting endomorphisms of valued fields / Auteur de la Conférence Dor, Yuval.
- [Multi angle] Ax-Kochen-Ershov principles for finitely ramified henselian fields / Auteur de la Conférence Dittmann, Philip.
- [Multi angle] Group construction in $C$-minimal structures / Auteur de la Conférence Delon, Françoise.
- [Multi angle] Homology groups in algebraically closed valued fields / Auteur de la Conférence Cubides Kovacsics, Pablo.
- [Multi angle] Existential uniform p-adic integration and descent for integrability and largest poles / Auteur de la Conférence Cluckers, Raf.
- [Multi angle] Polynomials that vanish on many sets of codimension 2 / Auteur de la Conférence Ben Yaacov, Itaï.
- [Multi angle] The model theory of Hardy fields and linear differential equations / Auteur de la Conférence Aschenbrenner, Matthias.
- [Multi angle] Transfer of decidability for existential theories of (valued) fields / Auteur de la Conférence Anscombe, Sylvy.
Bibliographie
- ASLANYAN, Vahagn, KIRBY, Jonathan, et MANTOVA, Vincenzo. A geometric approach to some systems of exponential equations. International Mathematics Research Notices, 2023, vol. 2023, no 5, p. 4046-4081. - https://doi.org/10.1093/imrn/rnab340
- ETEROVIĆ, Sebastian et HERRERO, Sebastián. Solutions of equations involving the modular 𝑗 function. Transactions of the American Mathematical Society, 2021, vol. 374, no 6, p. 3971-3998. - http://dx.doi.org/10.1090/tran/8244
- LI, Bao Qin et STEUDING, Jörn. Fixed points of the Riemann zeta function and dirichlet series. Monatshefte für Mathematik, 2022, vol. 198, no 3, p. 581-589. - http://dx.doi.org/10.1007/s00605-022-01709-x
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