CV:  Clic here for a 4 page CV (last updated in May 2023).

Research interests:

• In Commutative Algebra and Algebraic Geometry: Invariants of singularities for rings of characteristic p>0, differential operators on commutative rings, and applications to the problem of desingularization of algebraic varieties.

• In algebra and number theory: Zeta functions arising from algebraic counting problems such as the enumeration of subgroups in a group, or the enumeration of orders in a number field.

Preprints:

• (with C. del Buey) Purely inseparable extensions of rings. (arxiv)

Publications:

• (with C. del Buey and O. Villamayor) Differentiably simple rings and rings extensions defined by p-basis. Journal of Pure and Applied Algebra (2024) DOI:10.1016/j.jpaa.2024.107735  (arxiv) 

• On the degree of polynomial subgroup growth of nilpotent groups. Mathematische Zeitschrift (2023). DOI:10.1007/s00209-022-03156-8 (arxiv)

• (with J. Barrionuevo and P. Tirao) Deformations and rigidity in varieties of Lie algebras. Journal of Pure and Applied Algebra (2023) DOI:10.1016/j.jpaa.2022.107217

• Zeta functions of the 3-dimensional almost-Bieberbach groups.  Journal of Group Theory (2022).  DOI:10.1515/jgth-2021-0072 (arxiv)

• (with O. Villamayor) Multiplicity along primes of a radicial covering of a regular variety. Michigan Mathematical Journal  (2022) DOI: 10.1307/mmj/20195775 (arxiv)

• Zeta functions of virtually nilpotent groups.  Israel Journal of Mathematicas (2016). DOI:10.1007/s11856-016-1317-6 (arxiv)

Book chapters:

• (with O. Villamayor) An introduction to resulution of singularities via the multiplicity. in Singularities, Algebraic Geometry, Commutative Algebra and Related topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. Eds: G. -M. Greuel, L. Narv ́aez Macarro and S. Xamb ́o-Descamps. Springer Nature Switzerland AG (2018).(pdf) 

Other monographs:

• Funciones zeta de grupos.  PhD thesis. Advisors: Paulo Tirao-Karel Dekimpe (double PhD). 

• Funciones zeta de grupos. Notas de Cursos, V Encuentro Nacional de Algebra. 

Teaching: 

• 2023 Primer cuatrimestre. Teoría Algebraica de Números. Notes in Spanish.

• 2021 Primer cuatrimesre. Geometría Algebraica: Esquemas (FAMAF) y  Complementos de Análisis Matemático (FAMAF).

• 2019 Primer cuatrimestre. Análisis Matemático I (FCEFyN),  y Análisis Matemático III (FAMAF)

• 2018 Primer cuatrimestre. Matemática Discreta I, FAMAF.

• 2017 Segundo semestre. Análisis Matemático III, FAMAF

• 2016 Segundo semestre. Estructuras Algebraicas.  FAMAF.

• 2016 Primer semestre. Álgebra tensorial. Universidad Nacional de Colombia, Sede Manizales. Notes in Spanish