Research Center - Geometry at the Frontier


TEAM | Rubén A. Hidalgo

Rubén A. Hidalgo

Full Professor, Department of Mathematics and Statistics,
University of La Frontera

Education and Degrees
Habilitation, Bielefeld University, Bielefeld, Germany (1994)
Ph.D in Mathematics, SUNY at Stony Brook, New York, USA (1991)
Master of Science in Mathematics, Federico Santa María Technical University, Valparaíso, Chile (1987)
Bachelor in Mathematics, University of Santiago, Santiago, Chile (1986)

Curriculum Vitae
 +56 45 259 66 98

Research topics

Kleinian Groups
Holomorphic Dynamical Systems
Riemann Surfaces and their symmetries


On August 1988 I started my Ph.D. in Stony Brook University at New York under the supervision of Bernie Maskit (so I am officially one member of the Maskitiers). On April 1991 I defended my thesis, which concerned with the Schottky uniformizations of Riemann surfaces reflecting a given group of automorphisms. Starting 1991 I moved to Germany, more precisely to Bielefeld (so I am part of the Bielefeld’s conspiracy At Bielefeld University I joined the SFB-343: Discrete Structures in Mathematics (from 1991 to 1993) as a Scientific Collaborator under the supervision of Professors H. Helling and J. Mennicke. On 1992 I started the Habilitation process in Bielefeld and at the beginning of 1994 I have done my defense. On August 1993 I got a position at Universidad Técnica Federico Santa María (in the city of Valparaíso in Chile). I was very happy with my office, the window has a wonderful view to the Pacific ocean, which must say is not so pacific in winter!!. On 2015, following some of the other members of the geometry group, I moved to the Universidad de La Frontera (640 kilometers to the south from Valparaíso). So, I have changed the blue from the ocean to the dark green of the araucarias. Who known where I will be in the next years….. 

Selected Publications

Holomorphic differentials of Generalized Fermat curves
Hidalgo, Rubén A.
Journal of Number Theory. 2020, 217, pp. 78-101, DOI: 10.1016/j.jnt.2020.05.014

Geometric description of virtual Schottky groups
Hidalgo, Rubén A.
Bulletin of the London Mathematical Society. 2020, 52 (3), pp. 530-545, DOI: 10.1112/blms.12346

Regular dessins d'enfants with dicyclic group of automorphisms
Hidalgo, Rubén A.; Quispe, Saúl
Journal of Pure and Applied Algebra. 2020, 224 (5), pp., DOI: 10.1016/j.jpaa.2019.106242

Zapponi-orientable dessins d’enfants
Girondo, Ernesto; González-Diez, Gabino; Hidalgo, Rubén A.; Jones, Gareth
Revista Matemática Iberoamericana. 2020, 36 (2), pp. 549-570, DOI: 10.4171/rmi/1139

Real structures on marked Schottky space
Hidalgo, Rubén A.; Sarmiento, S.
Journal of the London Mathematical Society, 2018, 98 (2), pp. 253-274, DOI: 10.1112/jlms.12131


2019 - Yasmina Atarihuana - PhD in Sciences, mention in Mathematics | University of La Frontera, Temuco, Chile
Title: On the Connectivity of the branch and real locus of M_{0,[n+1]}.

2019 - Juan Carlos García - PhD in Sciences, mention in Mathematics | University of La Frontera, Temuco, Chile
Title: A remark on Z-orientability of Kleinian groups.

2017 - Sebastian Sarmiento - 
PhD in Mathematics | Federico Santa María Technical University, Valparaíso, Chile.
Title: Real structures on marked Schottky spaces.

2017 - Angélica Vega Moreno - PhD in Sciences, mention in Mathematics | University of Chile, Santiago, Chile.
Title: Superficies de Riemann y sus dessins d’enfants.

Research Grants

Joint USA-CHILE Geometry at the Frontier (
ANID, 2020 - 2022) – Principal Investigator.
Riemann surfaces, dessins d'enfants and origamis (Fondecyt, 2019 - 2023) – Principal Investigator.