Daniel Vargas-Montoya

I am an Assistant Professor in the Department Mathematics at the Universidad Nacional de Colombia, Bogotá (Unal). Previously, from December 2025 to May 2026, I was a postdocoral researcher at Max Planck Institut for Software Systems within the ERC DynAMiCs project , working with Florian Luca on analytic number theory. From December 2023 to November 2025, I was a postdoctoral researcher at the Institute of Mathematics of Toulouse (IMT) under the supervision of Charlotte Hardouin. Prior to that, I was a postdoc at IMPAN under the supervision of Masha Vlasenko from December 2021 to November 2023.

I got my PhD in mathematics from the Université Claude Bernard Lyon 1 in France, advised by Boris Adamczewski and Éric Delaygue.

My researche lies in number theory, with a primary focus on the arithmetic of differential equations, specifically algebracity modulo p, p-adic differential equations, the algebraic independence of G functions, and related topics. Here is my Cv.

Phd Thesis

Algébricité modulo p et structure de Frobenius forte [pdf ].

Papers and preprints:

Galois groups of Apéry-like series modulo primes with X. Caruso, F. Fürnsinn, and W. Zudilin. Bull. Aust. Math. Soc., 114(1): 65-78. 2026. [ArXiv]

On the algebraic independence of G-functions and E-functions, II: an effective version preprint (2025), arXiv:2502.204292, submitted.

On the algebraic independence of G-functions and E-functions, I: a p-adic criterion preprint (2025), arXiv:2502.00768, submitted.

Galois groups of reductions modulo p of D-finite series, with X. Caruso and F. Fürnsinn, preprint (2025), arXiv:250509429, 58 pp, submitted.

p-integrality of canonical coordinates, Acta Arith. 220 (2025) 229-261. [ArXiv]

Algebraicity modulo p of generalized hypergeometric series, J. Number Theory. 259 (2024), 273-321. [ArXiv ]

Strong Frobenius structure associated with q-difference operators, Ramanujan J. 67, 56 (2025) [ArXiv]

Monodromie unipotente maximale, congruences "à la Lucas" et indépendance algébrique, Trans. Amer. Math. Soc. 377 (2024), 167-202. [ArXiv ]

Algébricité modulo p, séries hypergéométriques et structures de Frobenius forte, Bull. Soc. Math. France. 149 (2021) 439-477. [ArXiv ].

Talks:

UN-Encuentro 70, Bogotá, Colombia, August 2026, Algebraicity (Congruences) Modulo p.
Rencontres arithmétiques de Caen: aspects p-adique et modulo p, Caen, France, June 2025, Algebraic Independence of E- and G-functions.
Workshop on Algebraicity and Transcendence for Singular Differential Equations, Vienna, Austria, October 2024, A p-adic Approach to Differential Equations.
Joint conference De rerum natura & Functional Equations and Interactions, Anglet, France, June 2024, Congruences modulo p, algebraic independence and monodromy.
Kolchin Seminar in Differenital Algebra, New York,Unitaed States, April 2024, Congruences modulo p, algebraic independence and monodromy. Video
Séminaire d'Algèbre et Géométrie, Versailles, France, March 2024, Monodromie, congruences et indépendance algébrique.
Workshop on differential equations in zero and positive characteristic, Lisboa, Portugal, February 2024, Algebraicity modulo p of diagonals and hypergeometric series.
Séminaire de théorie des nombres, Grenoble, France, January 2024, Monodromie, congruences et indépendance algébrique.
Séminaire de théorie des nombres, Toulouse, France, December 2023, Monodromie, congruences et indépendance algébrique
Séminaire de théorie des nombres, Bordeaux, France, November 2023, Monodromie, congruences et indépendance algébrique.
Journée en l'honneur de Gilles Christol , April 2023, q-strong Frobenius structure.
Warsaw Number Theory Seminar, March 2023, Algebraicity of hypergeometric functions modulo p.
Warsaw Number Theory Seminar, June 2022, q-strong Frobenius structure.
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. Video
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: daevargasmo@unal.edu.co