SPACE
I am a representation theorist working on Lie algebras and quantum groups. I am also interested in its geometric and combinatorial incarnations and their interactions with D-modules, Soergel bimodules and categorifications.
Papers
Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras. Journal of Algebra, 2023, in press. Joint with Vyacheslav Futorny and Kailash C. Misra.
Projective and Whittaker functors on category O. Journal of Algebra, 574 (2021), p. 154 - 171. Joint with Erik Backelin.
Derived counterparts of fusion categories of quantum groups. Journal of Algebra, 562 (2020), p. 257 - 285.
Higher Auslander-Reiten sequences and t-structures. Journal of Algebra, 459, (2016), p.280 - 308. Joint with Erik Backelin.
Preprints
The category of reduced imaginary Verma modules (joint with V. Futorny and A. de Oliveira) (submitted)
In preparation
A categorification of the Schur-Weyl duality. (With N. Libedinsky)
Combinatorial properties of Gelfand-Tsetlin modules. (With L. E. Ramirez and O. Morales)
Endomorphisms rings of projective and Whittaker modules. (With E. Backelin)
Twisted IVM, Kashiwara algebras and crystal bases. (with V. Futorny and K. C. Misra)
Expository papers
Introducción a los D-módulos (Divulgative paper, in spanish - With C. Rengifo). Lecturas Matemáticas, 42(2), 2021. Here.
Matemáticas por estudiantes: Una idea en movimiento. Revista Hipótesis (uniandes). 2015, v19, p28.
Una introducción al teorema de localización de Beilinson y Bersntein. (In spanish)
Translations
Kategorie O, perverse garben und moduln über den koinvarianten zur Weylgruppe. W. Soergel. Spanish translation here. English translation coming soon.
Talks
Una introducción a las categorificaciones de álgebras de Lie. Coloquios matemáticos. Universidad de Panamá (virtual, 25/04/24)
Álgebras de Lie y sus representaciones irreducibles. Workshop: Variedades exóticas y algo más. Univalle, Cali. (6/2/2024)
Categorificación. Seminario de jovenes investigadores. Uniandes, Bogotá. (23/11/2023)
Módulos de Verma imaginarios, sus categorías y cristales. Seminario de álgebra. Uniandes - UnalBog, Bogotá. (23/11/2023)
Cristales y módulos de Verma imaginarios. Seminario Institucional. UdeA - Medellín. (6/10/2023)
Crystal bases and imaginary Verma modules (Brazil - China Joint Mathematical Meeting) Foz do Iguaçu, Brazil. (17/7/2023)
Crystals and quantum groups (Seminário PosMat) UFABC. Santo André, SP, Brazil. (20/4/2023)
Crystal bases for imaginary Verma modules (XXVI Escola de Álgebra) UFPR. Curitiba, Brazil. (2/2/2023)
A derived approach to fusion categories. Seminário de Álgebra (Brazilian algebraic geometry seminar) IMPA. Rio de Janeiro, Brazil. (5/10/2022)
Some categories of representations and functors between them. III Álgebra em Natal. Natal, Brazil.(9/9/2022)
Classical, Quantum and Categorical. ICTP Workshop on Representation Theory and Applications. São Paulo, Brazil. (29/04/2022)
Derived fusion categories. Quantum symmetries student seminar (QSSS), The Ohio State University, USA. (16/04/2021)
Grupos cuánticos, categorías derivadas y anillos de fusión. Seminario de Categorías, UNAM, Mexico. (28/10/2020)
Representaciones irreducibles y cómo encontrarlas. Coloquio de matemáticas, Universidad de los Andes. Bogotá-Colombia. (12/03/2020).
Una introducción a la teoría de localización de álgebras de Lie. Seminario institucional, Universidad de Antioquia. Medellín - Colombia. (23/08/2019).
Derived fusion category of a quantum group. XXII Latin-American colloquium of algebra. (2017) Quito-Ecuador.
Some Derived Categories Related with Quantum Groups. XXI Colombian Congress of Mathematics, Bogotá, Colombia. 2017
Derived categories of quantum groups. Algebra Seminar, Universidad Federal Do Amazonas. Manaus - Brazil. (2017)
Combinatorics of quantum groups. Regional meeting for mathematics. Medellín - Colombia. 2016.
Higher Auslander-Reiten theory. XX Colombian Congress of Mathematics. Manizales - Colombia. 2015.