Daniel Vargas-Montoya
I am a postdoctoral research at Institute of Mathematics of Toulouse (IMT) under the supervision of Charlotte Hardouin. Previously, I was a postdoc at IMPAN under the supervision of Masha Vlasenko . I got my PhD in mathematics from the University of Lyon 1 in France. My advisers were Boris Adamczewski and Éric Delaygue.
I work in the area of number theory, I am mainly interested in the arithmetic of differential equations, namely algebracity modulo p, Frobenius structure, and eventually questions in regard to the algebraic independence of G functions.
Papers and preprints:
p-integrality of canonical coordinates, preprint (2023), arXiv:2306.03495, 27 pp, submitted.
Algebraicity modulo p of generalized hypergeometric series, J. Number Theory. 259 (2024), 273-321.
Strong Frobenius structure associated with q-difference operators, preprint (2022), arXiv:2201.06283, 45 pp, submitted.
Monodromie unipotente maximale, congruences "à la Lucas" et indépendance algébrique, Trans. Amer. Math. Soc. 377 (2024), 167-202. [pdf ]
Algébricité modulo p, séries hypergéométriques et structures de Frobenius forte, Bull. Soc. Math. France. 149 (2021) 439-477. [pdf ].
Talks:
Journée en l'honneur de Gilles Christol , April 2023, q-strong Frobenius structure.
Warsaw Number Theory Seminar, June 2022, q-strong Frobenius structure.
Study group: Differential equations and arithmetic, February 18, Existence of Frobenius structure for rigid differential equations.
Study group: Differential equations and arithmetic, February 4, Algebraicity of solutions modulo p.
Study group: Differential equations and arithmetic, January 21, Frobenius structure and its arithmetic consequences.
Warsaw Number Theory Seminar, May 2021, strong Frobenius structure, algebraicity modulo p, and G-functions.
Journée du séminaire différentiel, Versailles, France, Novembre 2020, structure de Frobenius forte, algébricité modulo p et indépendance algébrique. À cette occasion le séminaire s'est déroulé de manière virtuelle à cause de la situation sanitaire. Slides
Workshop on differential topology and related topics, New York, États Unis, Février 2020, Strong Frobenius structure, rigidity and hypergeometric equations. Slides,
Journée de l'équipe combinatoires et théorie des nombres, Institut Camille Jordan, Lyon, France, 28 janvier 2020, structure de Frobenius forte, rigidité et équations hypergéométriques.
Coloquio de matematicas Universidad Nacionale, sede Medellin, décembre 2019 , Ecuaciones diferenciales aritméticas
Conférence équations fonctionnelles et interactions, Anglet, France, juin 2019, structure de Frobenius forte, rigidité et équations hypergéométriques. Slides
Séminaire de doctorant et doctorantes, Institut Camille Jordan, Lyon, France, 29 d'avril 2019, Structure de Frobenius forte et séries transcendantes.
Contact Information:
e-mail: daniel.vargas-montoya@math.univ-toulouse.fr
Phd thesis
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Cv Daniel Vargas.pdf