Research and Publications

Journal Articles

• Baues-Wirsching cohomology and Svarc genus in small categories. Filomat. 2026 (to appear). (with I. Carcacía-Campos and E. Macías-Virgós).
• Varadarajan’s theorem on categorical distance in small categories. Math. Slovaca. 2026 (to appear). (with I. Carcacía-Campos and E. Macías-Virgós).
• Lefschetz fixed-object and fixed-morphism theorems for acyclic categories. Fixed Point Theory. 2026 (to appear). (with S. Castelo-Mourelle and E. Macías-Virgós).
• Integration with respect to the Lefschetz number. Journal of Fixed Point Theory and Applications. 2025. (with A.O. Majadas-Moure).
• 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

• Sheaf Theoretic Approach to Lefschetz Calculus. (with A.O. Majadas-Moure).
• Morse-Bott Inequalities for Endomorphisms. (with A.O Majadas-Moure, E. Macías-Virgós and J. Vilches).
• A combinatorial study of the fixed point index (with J.A. Álvarez-López and A.O Majadas-Moure).
• A Computational (Co)homological Approach to Contiguity Distance (wirh E. Macías-Vigós and A. Méndez-Vázquez).

Rencent or Future Conferences

• I have given the talk: Cálculo de Lefschetz: una nueva herramienta para el análisis topológico de datos. Jornadas de Topología de Datos 2026. Sevilla.
• I have given the talk: Integración con respecto al número de Lefschetz. Congreso Bienal de la Real Sociedad Matemática Española 2026. Sesión de la Red Española de Topología. Alicante.
• I (co)organize Differential, Algebraic, and Combinatorial Topology (May 7–8, 2026). A conference honoring the mathematical contributions of Enrique Macías Virgós, celebrating his 70th birthday. Santiago de Compostela.