Seminars
Past
2025
Highest Weight Categories (by Stephen Griffeth)
In this course we prove R. Rouquier's theorem on uniqueness of highest weight covers. (Notes)
2024
Kac-Moody Lie algebras
This is a problem solving weekly meeting where we provide solutions for the exercise sections of V. Kac's book Infinite dimensional Lie algebras.
Some solutions to the exercises, as well as elaborations on Kac's book can be found here.
2023
Representation theory of quivers
In this learning seminar, we cover the basics of the representation theory of quivers, in an algebro-geometric flavor.
Representation theory learning seminar
We cover the basics of representation theory of finite groups in positive characteristic and the representation theory of semisimple Lie algebras. You can find some incomplete (and not corrected) notes of the part about finite group representations here.
Affine Hecke algebras and orthogonal polynomials
This a learning seminar about affine Weyl groups, (double) affine Hecke algebras and orthogonal polynomials. We basically follow Macdonald's book with the same title.
Various materials
Solutions to The Rising sea: Foundations of Algebraic geometry (by Ravi Vakil)
(Solutions)
Notes on derived equivalences of representations (Notes)
Here are some notes in preparation about derived equivalences of categories of representations. So far I have only covered triangulated categories and the Gabriel-Zisman calculus of fractions, both necessary in order to study derived categories and derived functors.
The structure sheaf of an algebraic variety (Here)
This is a detailed proof of why we can always assume that the structure sheaf of an algebraic variety over a field k can be taken as a sheaf of functions on (the open subsets of) the variety, which is often assumed without major justification in most algebraic geometry books.
Minicourses
Separando conjuntos usando categorías. Yachay-Tech, 2025. (Notas, Videos)
Introducción a la teoría de representaciones de grupos compactos. Escuela de Álgebra AMARUN-UCE 2022. (Notas PDF)
Curso vacacional de Álgebra Abstracta. Aleph_0, Escuela Politécnica Nacional, 2021. (Videos)
Tableaux de Young. Minicursos AMARUN-USFQ 2021. (Notas PDF, Videos)
Curso vacacional de Topología General. Club de Matemática, Escuela Politécnica Nacional, 2021. (Videos)
Introducción a la teoría de representaciones de grupos finitos. Escuela de Álgebra AMARUN-EPN 2020. (Notas PDF)
Talks
Representation theory and the diagonal coinvariant ring for the type B Weyl group, XXIV Coloquio Latinoamericano de Álgebra, Pontificia Universidad Católica de Chile, Santiago, July 2024.
Teoría de representaciones y el anillo de coinvariantes diagonales del grupo de Weyl de tipo B, XXXVJ Jornadas de Matemática de la Zona Sur, Pontificia Universidad Católica de Temuco, Temuco, April 2024
Acciones metaplécticas sobre la complejificación del cono de Tits, Seminario no-degenerado (Seminario de estudiantes de matemática de la Universidad de Talca), Universidad de Talca, Talca, April 2024.
¿Qué tan avanzados somos para los aliens? - Un vistazo a los diagramas de Dynkin, Tertulia Matemática Yachay 2024, Yachay Tech, Urcuquí, January 2024.
Contando grafos usando teoría de representaciones. Escuela de verano de Matemáticas, Universidad de Talca, Talca, January 2024.
Automorphisms of double affine braid groups arising from topology. PhD research proposal, Universidad de Talca, Talca, November 2023.
(Double) affine Hecke algebras from a topological point of view. V Jornadas Ecuatorianas de Matemática, Yachay Tech, Ucurquí, November 2023.
Peinando trenzas en una galería. Seminario no-degenerado (Seminario de estudiantes de matemática de la Universidad de Talca), Universidad de Talca, Talca, November 2023.
Coinvariantes diagonales y el esquema de Hilbert de n puntos en el plano. Seminario no-degenerado (Seminario de estudiantes de matemática de la Universidad de Talca), Universidad de Talca, December 2022.
Representation theory and the diagonal coinvariant ring for the type B Weyl group. XVII Encuentro de Matemática y sus Aplicaciones - IV Jornadas Ecuatorianas de Matemática, Escuela Politécnica Nacional, Quito, November 2022.
Ecuaciones diferenciales: una perspectiva algebraica. Escuela de Álgebra AMARUN-UCE 2022.
Representaciones diagonalizables finito-dimensionales del álgebra de Cherednik racional ciclotómica. Escuela Superior Porlitécnica del Litoral. Guayaquil, December 2021.
Finite dimensional diagonalizable representations of cyclotomic rational Cherednik algebras. Master's thesis dissertation. July 2021.
Categoría O para el álgebra de Cherednik racional. Seminario Relajao', Universidad de Chile, Santiago de Chile, 2020. (Video)