Research and Publications

Journal Articles

• Morse-Bott Theory on posets and a homological Lusternik-Schnirelmann Theorem. Journal of Topology and Analysis. 2024. (with D. Fernández Ternero, E. Macías-Virgós and J. A. Vilches).
• Poincaré duality for posets. Topology and its Applications. 2023. (with E. Macías-Virgós and J. A. Vilches).
• m-homotopic distance. Topology and its Applications. 2023. (with E. Macías-Virgós and J. Oprea).
• Fundamental Theorems of Morse Theory on posets. AIMS Mathematics. 2022. (with D. Fernández Ternero, E. Macías-Virgós, J. A. Vilches and N. Scoville).
• Homotopic Distance and Generalized Motion Planning. Mediterranean Journal of Mathematics. 2022. (with E. Macías-Virgós and M. J. Pereira-Sáez).
• Homotopic distance between maps. Math. Proc. Cambridge Philos. Soc. 2021. (with E. Macías-Virgós).
• Homotopic distance between functors. Journal of Homotopy and Related Structures. 2020. (with E. Macías-Virgós).

Preprints

• Integration with respect to the Lefschetz number. (with A.O. Majadas-Moure).
• Sheaf Theoretic Approach to Lefschetz Calculus. (with A.O. Majadas-Moure).
• Lefschetz fixed-object and fixed-morphism theorems for acyclic categories. (with S. Castelo Mourelle and E. Macías-Virgós).
• Varadarajan’s Theorem for categorical distance. (with I. Carcacía-Campos and E. Macías-Virgós).

Books

• Morse Theory on Finite Spaces. Publicaciones del Departamento de Geometría y Topología. Universidade de Santiago de Compostela. 2023.
• Integración con respecto a la característica de Euler-Poincaré. Publicaciones del Departamento de Geometría y Topología. Universidade de Santiago de Compostela. ISBN 978-84-89390-50-8. 2018. (in Spanich).

Book Chapters

• Robótica topológica. Actas do Seminario de Iniciación á Investigación. As matemáticas do veciño. Universidade de Santiago de Compostela. ISBN: 2171-6536. pp. 9 - 15. 2017.
• Teoría de Morse: Relacionando dinámica e topoloxía. Libro de resumos correspondentes ás presentacións durante o VI Encontro da Mocidade Investigadora - Ciencias. ISBN: 978-84-09-03154-2. pp. 9 - 15. 2018. (in Galician).

Divulgation

• Robótica topológica. TEMat. 2017. (In Spanish).

Editor

• Actas del VIII Encuentro de Jóvenes Topólogos. Actas del VIII Encuentro de Jóvenes Topólogos. 3, Real Sociedad Matemática Española. 2021.
• As matemáticas do veciño. Actas do Seminario de Iniciación á Investigación 2019-2020. Universidade de Santiago de Compostela. 2020.

Rencent Talks at Conferences

• Algebraic and Discrete Morse Theories. VII Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española. Bilbao, Spain. 2025.
• From Euler Calculus to Lefschetz Calculus? European Congress of Mathematics. MS: Applied and Combinatorial Topology. Sevilla, Spain. 2024.
• Homotopic Distance between maps I. Geometry, One Day Meeting on Topology and its Applications. Braga, Portugal. 2024.