Estudios:

• January 2006: Licenciado en Matemática, Universidad Autónoma Tomás Frías (Bolivia). Advisor: M.Sc. Orlando Romano. Title: Cohomologia de Khovanov en nudos alternantes. 
• November 2009: Magíster en Ciencias con mención en Matemática, Universidad de Talca (Chile), Graduación con Examen General (Escrito y Oral). 
• June 2013: PhD in Mathematics, Universidad de Concepción (Chile). Advisor: Dra. Michela Artebani. Title: Fields of moduli and fields of definition of projective algebraic varieties.

Cursos Dictados:  

2023 - Universidad de La Frontera (Temuco - Chile)

• History of Mathematics ( Undergraduate students)
• Matemathic II (Undergraduate students)
• Algebraic structures II (Undergraduate students)

2022 - Universidad de La Frontera (Temuco - Chile)

• Measure theory (Graduate students)
• Numerical sets (Undergraduate students)
• Algebraic structures I (Undergraduate students)

2021 - Universidad de La Frontera (Temuco - Chile)

• Algebraic structures I (Graduate students)
• Functional analysis (Graduate students)
• Algebraic structures II (Undergraduate students)

2020 - Universidad de La Frontera (Temuco - Chile)

• Topology (Graduate students)
• Algebraic structures I (Undergraduate students)
• Linear algebra (Undergraduate students)

2019 - Universidad de La Frontera (Temuco-Chile)

• Introduction to Riemann surfaces and algebraic curves (Graduate students)
• History of mathematics (Undergraduate students)
• Numerical sets Linear algebra (Undergraduate students)
• Linear algebra (Undergraduate students)
• Precalculus (Undergraduate students)

2018 - Universidad de La Frontera (Temuco-Chile)

• Numerical sets (Undergraduate students)
• Theory of numbers (Undergraduate students)
• Linear algebra (Graduate students) 
• Basic and Algebraic Topology (Graduate students) 

2017 - Universidad de La Frontera (Temuco-Chile)  

• Functional analysis (Graduate students)

2017 - Universidad Central (Quito-Ecuador)

• Functional analysis (Graduate students) 

2016 - Universidad de La Frontera (Temuco-Chile) 

• Basic and algebraic topology (Graduate students)

2015 - Universidad de La Frontera (Temuco-Chile)

• Real analysis (Graduate students) 

2015 - Universidad Central (Quito-Ecuador)

• Real analysis (Graduate students) 

2013 - Universidad de Concepción (Concepción-Chile) 

• 2013, Calculus for Forest Engineering (Undergraduate students)
• Mathematics II for Forest Engineering (Undergraduate students)
• Elements of Mathematics for Anthropology (Undergraduate students)

2012 - Universidad de Concepción (Concepción-Chile) 

• Calculus for Forest Engineering (Undergraduate students)
• Mathematics II for Forest Engineering (Undergraduate students)

2011 - Universidad de Concepción (Concepción-Chile)

• Mathematics for veterinary medicine (Undergraduate students)
• Calculus I (Undergraduate students)

2010 - Universidad de Concepción (Concepción-Chile)

• 2010, Calculus I (Undergraduate students)

Teaching assistant

• 2016, Real analysis (Graduate students), Universidad de La Frontera (Temuco-Chile)
• 2015, Basic Topology (Graduate students), Universidad Central (Quito-Ecuador)
• 2015, Basic Topology (Graduate students), Universidad de La Frontera (Temuco-Chile)
• 2014, Algebraic topology (Graduate students), Universidad Técnica Federico Santa María (Valparaíso-Chile)
• 2009-2010, Calculus III (Undergraduate students), Universidad de Concepción (Concepción-Chile)
• 2007-2008, Calculus I, Algebra I, Linear algebra (Undergraduate students), Universidad de Talca (Talca-Chile)
• 2002-2006, Plane geometry, Algebra I (Undergraduate students), Universidad Autónoma Tomás Frías (Potosí-Bolivia),

Conferencias y Ponencias:

Charlas: Algunas de mis charlas relevantes

2023

• Dessins d’enfants and some holomorphic structures on the Loch Ness monster, Workshop on surfaces in the frontier, Universidad Nacional de Colombia (sede Manizales), February 2023, Manizales (Colombia).
• Ends space of the fiber product over inifinite-genus Riemann surfaces, XXXV Jornada de Matemática de la Zona Sur, Universidad de Concepción, April 2023, Concepción (Chile)

2022

• Cuerpo de móduli versus cuerpos de definición de curvas, V Congreso Matemático Estudiantil, Universidad Autónoma Tomás Frías, October 2022, Potosí (Bolivia), via Zoom.
• Generalized superelliptic Riemann surfaces, XXXIV Jornada de Matemática de la Zona Sur, Universidad de Los Lagos, April 2022, Osorno (Chile), via Zoom.
• Superficies de Riemann superelípticas generalizadas, XVII Encuentro de Matemática y sus aplicaciones y las IV Jornadas Ecuatorianas de Matemática, Escuela Politécnica Nacional de Quito (Ecuador), November 2022, Quito (Ecuador), via Zoom.
• Generalized quasi-dihedral group acting on pseudo-real Riemann surfaces, Encuentro de geoemtría compleja y dina ́mica holomorfa-aritm ́etica 2022, Facultad de Ciencias de la Uni- versidad Austral de Chile, November 2022, Valdivia (Chile)

2021

• Cuerpo de móduli vs cuerpos de definición de funciones racionales, Segunda escuela de geometría, Facultad de ciencias, Universidad Central del Ecuador, July 2021, Quito (Ecuador), via Zoom.
• Dessins d'enfants and some holomorphic structures on the Loch Ness monster, USA-Chile Workshop on Hyperbolic geometry, June 2021, (Temuco, Chile) via zoom. 
• Connectedness of some subspaces of the moduli space of rational maps, XXXIII Jornada de Matemática de la Zona Sur, April 2021, (Temuco, Chile) via Zoom.

2020

• Grupos dicíclicos como grupo de automorfismos de superficies de Riemann, Seminario de "Iniciación científica", Universidad Nacional de Colombia (sede Manizales), February 2020, Manizales (Colombia)
• Introducción a Superficies de Riemann, cursillo de "Iniciación científica", Universidad Nacional de Colombia (sede Manizales), February 2020, Manizales (Colombia)
• Cuerpo de móduli versus cuerpos de definición de curvas, Primera escuela de geometría, Facultad de ciencias, Universidad Central del Ecuador, Jun 2020, Quito (Ecuador), via Zoom.

2019

• Field of moduli vs fields of definition for dynamical systems on PN , Seminario Aritmética y Geometría en Valparaíso, March 2019, Valparaíso (Chile) 
• Regular Dessins D’enfants with Dicyclic group of automorphisms, XXXII Jornada de Matemática de la Zona Sur, April 2019, Punta Arenas (Chile). 

2018

• On pseudo-symmetric p-hyperelliptic Riemann surfaces, XXXI Jornada de Matem ́atica de la Zona Sur, April 2018, Valdivia (Chile). 
• Connectedness of same subspaces of the moduli space of rational maps, Encuentro de Geometría y Dinámica Holomorfa-Aritmética, December 2018, Los Angeles (Chile).
• The field of moduli vs fields of definition for dynamical systems on P1, Encuentro de Geometría y Dinámica Holomorfa-Aritmética, December 2018, Los Angeles (Chile). 
• Polígonos regulares, MATEA 2018, Diciembre 2018, Santiago (Chile). 

2017

• Automorphism groups of pseudo-real Riemann surfaces, XXX Jornada de Matemática de la Zona Sur, April 2017, Concepción (Chile). 
• Automorphism groups of pseudo-real Riemann surfaces, XXII Coloquio Latinoamericano de Álgebra, August 2017, Quito (Ecuador).
• Riemann surfaces defined over the reals, LXXXVI Encuentro Anual Sociedad De Matemática De Chile, November 2017, Talca (Chile).
• Rational maps not definable over their field of moduli, Encuentro de Geometría Compleja y Dinámica Holomorfa-Aritmética, November 2017, Valparaíso (Chile). 

2016

• Generalized quaternion groups as groups of automorphisms of Riemann surfaces, XXIX Jornada de Matemática de la Zona Sur, April 2016, Santa Cruz (Chile).
• 2-groups as full automorphism group of pseudo-real Riemann surfaces, SUMA 2016 (primer encuentro conjunto de la sociedad de matemática de Chile y la unión matemática Argentina), December 2016, Valparaíso (Chile).

2015

• Pseudo-real rational maps, Encuentro de Sistemas dinámicos en Valdivia, June 2015, Valdivia (Chile).
• Automorphisms of Pseudo-real Riemann surfaces, LXXXIV Encuentro Anual Sociedad De Matemática De Chile, November 2015, Pucón (Chile).
• Grupo de automorfismos de superficies de Riemann pseudo-reales de género 5, International Workshop: Perspectives in Geometry 2, December 2015, Temuco (Chile). 

2014

• Fields of moduli and fields of definition of odd signature curves, Liberdade Em Geometria Algébrica LEGAL 2014, February 2014, Teresópolis, Rio de Janeiro (Brasil).
• Riemann surfaces defined over the reals, XXVII Jornada de Matemática de la Zona Sur, Abril 2014, Trailanqui (Chile). 
• Field of moduli vs fields of definition of curves, International Workshop: Perspectives in Geometry, December 2014, Valparaíso (Chile). 

2013

• Cuerpo de móduli vs cuerpos de definición de curvas, 2do. Encuentro matemática del Bío- Bío, January 2013, Concepción (Chile).
• Cuerpos de móduli de curvas, XXVI Jornada de Matemática de la Zona Sur, April 2013, Termas Quinamávida (Chile). 
• Invariantes diedrales de curvas hiperelpticas, LXXXII Encuentro Anual Sociedad De Matemática De Chile, November 2013, Olmué (Chile).
• Field of moduli and fields of definition of non-hyperelliptic curves, Jornada de tesistas en Aritmética y Geometría , November 2013, Valparaiso (Chile). 

2012

• Póster: Fields of moduli and fields of definition of odd signature curves, XXV Jornadas de Matemática de la Zona Sur, April 2012, Concepción (Chile). 

2011

• Cuerpo de móduli y definición de curvas de signatura impar, XXIV Jornadas de Matemática de la Zona Sur, April 2011, Pucón (Chile). 
• Cuerpo de móduli vs cuerpo de definición de cuárticas planas, LXXX Encuentro Anual SoMaChi, November 2011, Los Andes (Chile).
• Cuerpo de móduli vs cuerpo de definición de curvas p-gonales cíclicas, IX Encuentro de Geometría Compleja y Sistemas Dinámicos UTFSM, November 2011, Valparaiso (Chile). 

Papers:

2022

• Dessins d'enfants and some holomorphic structures on the Loch Ness monster, with Y. Atarihuana, J.C. García, R. A. Hidalgo and C. Ramirez-Maluendas, Quarterly Journal of Mathematics, (2022),  349–369.

2021

• On real and pseudo-real rational maps, with R. A. Hidalgo, Nonlinearity, 34 (2021), 6248-6272. 

2020

• Regular dessins d'enfants with dicyclic group of automorphisms, with Ruben A. Hidalgo, Journal of Pure and Applied Algebra, 224 (2020), no. 5, 106242 

2018

• Riemann surfaces defined over the reals, with Eslam Badr and Ruben A. Hidalgo, Archiv der Mathematik 110 (2018), 351–362. 
• A note on the connectedness of the branch locus of rational maps, with R. A. Hidalgo, Glasgow Mathematical Journal 60 (2018), no. 1, 199–207. 
• Rational points in the moduli space of genus two, with L. Beshaj, R. Hidalgo, S. Kruk, A. Malmendier, and T. Shaska. Higher genus curves in mathematical physics and arithmetic geometry, 83–115, Contemporary Mathematics 703, Amer. Math. Soc., Providence, RI, (2018). 

2017

• Automorphism group of pseudo-real Riemann surfaces, with M. Artebani and C. Reyes, Journal of Pure and Applied Algebra 221 (2017), no. 9, 2383–2407. 
• Regular dessins d’enfants with field of moduli Q(\sqrt[p]{2}), with R. A. Hidalgo, Ars Mathematica Contemporanea 13 (2017), no. 2, 323–330. 
• Quasiplatonic curves with symmetry group Z^2xZm are definable over Q, with R. A. Hidalgo, L. Jimenez, S. Reyes-Carocca, Bulletin of the London Mathematical Society 49 (2017), 165– 183.
• A tower of Riemann surfaces which cannot be defined over their field of moduli, with R. A. Hidalgo, M. Carvacho, M. Artebani, Glasgow Mathematical Journal 59 (2017), no. 2, 379–393.

2016

• Jacobian variety of generalized Fermat curves, with R. A. Hidalgo and M. Carvacho, Quar- terly Journal of Mathematics 67 (2016), no. 2, 261–284. 
• Fields of moduli of some special curves, with R. A. Hidalgo, Journal of Pure and Applied Algebra 220 (2016), 55–60.

2012

• Fields of moduli and fields of definition of odd signature curves, with M. Artebani, Archiv der Mathematik 99 (2012), 333–344.

Preprints:

• On generalized superelliptic Riemann surtaces, with Ruben A. Hidalgo and Tony Shaska. 
• 2-groups as automorphism group of Riemann surfaces.  
  

Áreas de Interés:

Mis intereses de investigación:

• Fields of moduli and fields of definition.
• Riemann and Klein surfaces
• Fuchsian and NEC groups.
• Projective algebraic varieties, Abelian varieties
• Planar surfaces.
• Dynamical systems (rational dynamics). 

Hobbies:  

• Deporte: Atletismo.