Algebraic groups and homogeneous spaces, rational points, Hasse principle, weak approximation, Galois cohomology.

PhD students' thesis:

Student's name: Claudio Bravo.
Institution: Universidad de Chile.
Thesis title: Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups.
Defense date: March 4, 2022.

Master students' thesis:

Student's name: Felipe Gambardella
Institution: Universidad de Chile.
Thesis title: Aproximación débil para espacios homogéneos sobre cuerpos globales geométricos.
Defense date: January 27, 2022.

Student's name: Gary Martínez
Institution: Universidad de Chile.
Thesis title: Fibrados asociados a cocientes suaves de variedades abelianas
Defense date: March 9, 2021.

Student's name: Felipe Rivera
Institution: Universidad de Chile.
Thesis title: Propiedades de aproximación en cohomología galoisiana de grupos finitos
Defense date: March 5, 2021.

Student's name: Pablo Quezada
Institution: Pontificia Universidad Católica de Chile.
Thesis title: Cocientes suaves de superficies abelianas por grupos finitos
Defense date: January 22, 2019.

Bachelor students' thesis (or equivalent):

Student's name: Bruno Aguiló
Institution: Universidad de Chile
Thesis title: Cocientes étale de toros complejos
Defense date: July 2020

Student's name: Juan Pablo Llerena
Institution: Universidad de Chile
Thesis title: Números p-ádicos y el Teorema de Kronecker-Weber
Defense date: July 2020

Student's name: Felipe Gambardella
Institution: Universidad de Chile
Thesis title: Haces, sitios, topos y álgebra homológica
Defense date: December 2019.

Student's name: Gary Martínez
Institution: Universidad de Chile
Thesis title: Clasificación de grupos algebraicos conexos de pequeña dimensión
Defense date: December 2018.

Student's name: Felipe Rivera
Institution: Universidad de Chile
Thesis title: Formas cuadráticas sobre cuerpos locales y globales
Defense date: July 2018.

Student's name: Ian Bellet
Institution: Universidad de Chile
Thesis title: Variedades abelianas
Defense date: July 2018.

Important conferences to which I have been invited:

Subplenary talk at the "XXVIII Congreso de Matemáticas Capricornio", 28/07 – 30/07 2021, Copiapó, Chile.
"Emerging Research in Algebraic Groups, Motives, and K-Theory", 09/09 – 13/09 2019, Saint Petersburg, Russia.
“Algebraic Groups: Geometry, Actions and Structures”, 29/10 – 02/11 2018, Lyon, France.
“SUSTech Young Mathematicians Academic Forum (On the occasion of the tenth anniversary of Séminaire Mathjeunes)”, 23/07 – 28/07 2018, Shenzhen, China.
Subplenary talk at the "LXXXVI Encuentro Anual SOMACHI", 02/11 – 04/11 2017, Talca, Chile.

Other academic activities:

- Organizer of the weekly seminar "Santiago Number Theory and Algebra Seminar" since 2018.
- Organizer of the weekly math colloquium "Coloquio Las Palmeras" at Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, 2020-2021.
- Member of the organizing committee for the "Fourth Latin American School on Algebraic Geometry and its Applications", Universidad de Talca, December 2019.
- Member of the scientific and organizing committees for the "V Encuentro Chileno de Teoría de Números", Universidad de Chile, May 2018.

Outreach activities:

I have participated in the following activities in Chile:
- "Verano Matemático en Las Palmeras: Escuela remota 2022" (online summer school for middle and high school students)
- "Te lo cuento en 5 minutos" (https://telocuentoen5min.wixsite.com/website)
- "Club de Matemática" at Academia Narvezzi (https://www.academianarvezzi.com/club-de-matematica)
- "Delivery Matemático" at Ciencia Delivery (https://sites.google.com/colegiosb.cl/ciencias-delivery)
- Talk to 8th grade students at Thomas Jefferson STEM School.
- Mathematical Week 2019 at Colegio Calasanz.
- 3rd Math camp "MateA" (math camp for girls in high school).
- Mathematical Week 2018 at Colegio Calasanz.

I have participated in the following activities in France:
- Organizer of the highschool maths tournament TFJM2 “Tournoi Français des Jeunes Mathématiciennes et Mathématiciens from 2013 to 2017.
- "Animath" summer school 2017 on preparation for math olympics: course on number theory.
- "Parimaths" maths club for highschool students in Paris: several talks given between 2013 and 2016.
- Fête de la Science 2015 and 2016 at École polytechnique: entertaining a stand on pure mathematics.
- Chief editor of the book “Introduction aux Mystères” by Misha Gromov. 2012
- Adjoint curator of the exhibition "Mathematics - A beautiful Elsewhere" at the Fondation Cartier pour l'art contemporain. October 2011 - March 2012.