Algebra, geometry, algebraic geometry, abelian varieties, curves, Riemann surfaces, moduli spaces

Theses I have supervised:

Master's:

1. Nelson Alvarado, Universidad de Chile. "Compactificaciones del espacio de moduli de superficies abelianas no simples." Expected defense date: July 2021.
2. Gary Martínez, Universidad de Chile. "Fibrados asociados a cocientes suaves de variedades abelianas." Defense date: March 9, 2021.
3. Sebastián Rahausen, Universidad de Chile. "Subespacios de Galois para la curva racional normal". Defense date: January 30, 2019.
4. Pablo Quezada, Pontificia Universidad Católica de Chile. Cotutor, along with Giancarlo Lucchini Arteche. "Cocientes suaves de superficies abelianas por grupos finitos". Defense date: January 22, 2019.
5. Matías Alvarado, Universidad de Chile. "Puntos fijos de endomorfismos de toros complejos". Defense date: March 11, 2018.

Doctorate:

1. José Aburto, Universidad de Chile. Expected defense date: September 2022.
2. Camila Muñóz, Universidad de Chile. Expected defense date: December 2021.

Undergraduate research units:

1. Mathias Ortiz, first semester 2021. "Cotas para el juego de Ducci".
2. Marcelo Riveros, first semester 2021. "Leyes de grupo en curvas afines".
3. Sebastián Rosselot, first semester 2021. "Sobre subespacios de Galois para la curva racional normal".
4. Javier Pávez Cornejo, first semester 2021. "Teoría de grupos y música".
5. Rebeca Huerta, second semester 2020. "Geometría algebraica".
6. Juan Pablo Llerena, second semester 2020. "Inmersiones de Galois de curvas de género 2".
7. Joaquín Oyarzún, first semester 2020. "Criptografía de curvas elípticas".
8. Bruno Aguiló, first semester 2020. "Acciones libre de grupos finitos en toros complejos". I cotutored the student along with Giancarlo Lucchini Arteche.
9. Joaquín Oyarzun, second semester 2019. "Álgebra conmutativa".
10. Nelson Alvarado, first semester 2019. "Sobre la clasificación birracional de superficies algebraicas".
11. Ian Bellet, first semester 2018. "Variedades abelianas".
12. Fabián Rivera, first semester 2014. "Grupos Fuchsianos".

Undergraduate monographs:

1. Joaquín Oyarzún and Catherine Lemún, second semester 2018. "Introducción a las curvas elípticas".

Dissemination:

1. Talk (on Zoom) for undergraduate students of the Facultad de Ciencias of the Universidad de Chile titled "Una introducción entretenida y elemental a los espacios de móduli". October 13, 2020.
2. I recorded a talk titled "Explorando el mundo de las cónicas" for the website of the math camp MateA.
3. Organizer of the math camp MateA 2020 for female high school students, January 2020.
4. Talk at the Narvezzi Academy in Rancagua, Chile, titled "¿Qué es la verdad?". October 2019.
5. Talk at the school Colegio Calasanz de Ñuñoa for 11th grade students, titled "Criptografía". May 16, 2019.
6. Organizer of the math camp MateA 2018 for female high school students, December 2018.
7. Talk at the school Colegio Calasanz de Ñuñoa for 11th grade students, titled "Teselaciones". May 17, 2018.
8. Participant of the math camp MateA 2017 for female high school students, January 2018.
9. Participant of the math camp MateA 2016 for female high school students, January 2017.
0. Participant of the activity "El Científico va a la Calle", which took place in the Plaza de Armas de Santiago, organized by the Facultad de Ciencias of the Universidad de Chile. September 2, 2015.

Organization of schools and conferences:

1. Organizer of A Workshop on Abelian Varieties, a conference that was to be held in Rome, Italy, between August 26 and 28 of 2020, but the conference has been postponed until further notice because of the pandemic.
2. Organizer of the VIII Iberoamerican Congress on Geometry in Morelia which was to be held between June 22 and 26, 2020. Unfortunately it was postponed until further notice because of the coronavirus pandemic.
3. Organizer of the algebraic geometry session for the SOMACHI conference that was to be held between November 13 and 15, 2019. Unfortunately due to political unrest in the country, the conference was cancelled.
4. Organizer of the workshop Geometry at the Frontier II. November 15-17, 2017. Pucón, Chile.
5. Organizer of the school Geometry at the Frontier II. November 13-15, 2017. Pucón, Chile.
6. Organizer of the algebraic geometry and commutative algebra session of the XXII Coloquio Latinoamericano de Álgebra. August 7-11, 2017. Quito, Ecuador.
7. Organizer of the workshop Geometry at the Frontier I, in Memory of Alexander Vasil'ev. November 16-18, 2016. Pucón, Chile.
8. Organizer of the school Geometry at the Frontier I. 14-16 of November, 2016. Pucón, Chile.

International visits:

1. Universidad Autónoma de Zacatecas. Zacatecas, Mexico. October 7-12, 2019.
2. Università degli Studi Roma Tre. Roma, Italy. April 27, 2017. I visited Giulio Codogni.
3. Università degli Studi di Roma "La Sapienza". Roma, Italy. April 18-29, 2017. I visited Riccardo Salvati Manni.
4. Tata Institute of Fundamental Research. Mumbai, India. March 7-18, 2016. I visited Indranil Biswas.
5. Universidad Autónoma de Zacatecas. Zacatecas, Mexico. August 17-22, 2015.

Selected presentations:

1. Inmersiones de Galois de curvas suaves proyectivas. Jornadas Matemáticas de la Zona Sur 2021, 24, 2021.
2. Cocientes suaves de variedades abelianas. Weekly colloquium at the Departamento de Matemáticas of the Facultad de Ciencias of the Universidad de Chile. May 13, 2020.
3. Rectas trisecants de la variedad de Kummer y la aplicación de Gauss. Algebraic geometry seminar at the Universidad Autónoma de Zacatecas, October 8, 2019.
4. Rectas trisecantes y el problema de Schottky. Talk for the weekly colloquium at the Departamento de Matemáticas y Estadística, UFRO, May 23, 2019.
5. Trisecantes de la variedad de Kummer de una variedad Jacobiana. Seminario SaNTAS, April 16, 2019.
6. Smooth quotients of abelian varieties. Brazil-Chile-Mexico, BCM-Singularities, 4th meeting on singularities, Universidad de Talca, March 11-15, 2019.
7. Divisores theta cuya aplicación de Gauss tiene una fibra de dimensión positiva. Congreso SOMACHI 2018, Rancagua, Chile.
8. Galois embeddings of abelian varieties and a question raised by Ekedahl-Serre. Università degli Studi Roma Tre. April 2017.
9. Galois embeddings of abelian varieties and a question raised by Ekedahl-Serre. Università degli Studi Roma "La Sapienza". April 2017.
10. Galois embeddings of abelian varieties. Congreso SUMA 2016, Valparaíso, Chile.
11. Torsion points on theta divisors. Jornadas Matemáticas de la Zona Sur 2016, Santa Cruz, Chile.
12. Sobre dos formas de descomponer una variedad abeliana. Zacatecas, Mexico. August 2015.
13. Non-simple abelian varieties. Congreso COMCA 2015, Iquique, Chile.
14. Non-simple principally polarized abelian varieties. Iberoamerican Congress on Geometry, June 2014. New York City, New York.
15. Variedades abelianas principalmente polarizadas no simples. Jornadas Matemáticas de la Zona Sur 2014, Trailanqui, Chile.