Galois differential Theories and transcendence Thematic Month Week 4 / Théories de Galois différentielles et transcendance Mois thématique semaine 4

Collection Galois differential Theories and transcendence Thematic Month Week 4 / Théories de Galois différentielles et transcendance Mois thématique semaine 4

Organizer(s) Dreyfus, Thomas ; Poulet, Marina ; Rond, Guillaume ; Wibmer, Michael

Date(s) 17/02/2025 - 21/02/2025

linked URL https://conferences.cirm-math.fr/3270.html

00:00:00 / 00:00:00

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Regular singularities of Mahler systems

By Marina Poulet

The density theorem of Schlesinger ensures that the monodromy group of a differential system with regular singular points is Zariski-dense in its differential Galois group. We have analogs of this result for difference systems such as q-difference and Mahler systems, whose only assumption is the regular singular condition. Moreover, solutions of difference or differential systems with regular singularities have good analytical properties. For example, the solutions of differential systems which are regular singular at 0 have moderate growth at 0. We have general algorithms for recognizing regular singularities and they apply to many systems such as differential and q-difference systems. However, they do not apply to the Mahler case, systems that appear in many areas like automata theory. We will explain how to recognize regular singularities of Mahler systems. It is a joint work with Colin Faverjon.

Information about the video

Date of recording 17/02/2025
Date of publication 07/03/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20308503
Cite this video Poulet, Marina (17/02/2025). Regular singularities of Mahler systems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20308503
URL https://dx.doi.org/10.24350/CIRM.V.20308503

Domain(s)

Bibliography

FAVERJON, Colin et POULET, Marina. An algorithm to determine regular singular Mahler systems. arXiv e-prints, 2021, p. arXiv: 2102.10842. - [http:// https://doi.org/10.48550/arXiv.2102.10842](http:// https://doi.org/10.48550/arXiv.2102.10842)

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