My research focuses on problems of Differential Geometry with extra symmetry assumptions. I am mainly interested in:
Homogeneous geometry.
Lie theory.
Geometric Invariant Theory applied to geometry.
My articles on Arxiv.
"The mean curvature flow of subgroups on Lie groups of dimension three" with Gabriela P. Ovando, Mariel Sáez. Available on arXiv:2505.17892.
"Almost abelian complex nilmanifolds" with Adrián Andrada, María L. Barberis, Sönke Rollenske, Konstantin Wehler. Available on arXiv:2502.03306.
"Classification almost abelian Lie groups admitting left-invariant complex or symplectic structures" with María L. Barberis, Verónica S. Díaz, Yamile Godoy, Isabel Hernández. To appear in The Journal of Geometric Analysis. Available on arXiv:2406.06819.
"The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups" with Mark Gould & Artem Pulemotov. Communications in Analysis and Geometry, Volume 32 (2024), Number 5, 1445–1480.
"On the signature of the Ricci curvature on nilmanifolds" with Ramiro Lafuente. Transformation groups, Volumen 29 (2024), 1-15. https://doi.org/10.1007/s00031-021-09686-5.
"The mean curvature flow on solvmanifolds'' with Gabriela P. Ovando, Raquel Perales, Mariel Sáez. Boletín de la Sociedad Matemática Mexicana, 30 (39) (2024). https://doi.org/10.1007/s40590-024-00612-9.
"SKT structures on nilmanifolds" with Marina Nicolini. Mathematische Zeitschrift, 302 (2022), 1307--1320. https://doi.org/10.1007/s00209-022-03107-3
"The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups" with Artem Pulemotov & Wolfgang Ziller. Differential Geometry and its Applications, 78 (2021), article 101794.
"The long-time behavior of the homogeneous pluriclosed flow" with Ramiro Lafuente. Proceedings of the London Mathematical Society , 119 (3) (2019), 266-289.
"The Alekseevskii conjecture in low dimensions" with Ramiro Lafuente. Mathematische Annalen , 367 (1) (2017), 283-309.
"Homogeneous Ricci solitons in low dimensions" with Ramiro Lafuente. International Mathematics Research Notices , 2015 13 (2015), 4901-4932.
"The Ricci flow in a class of solvmanifolds" Differential Geometry and its Applications , 31 (2013) 472-485.
"Filiform nilsolitons of dimension 8" Rocky Mountain Journal of Mathematics , 41 (2011), 1025-1043.
"Sobre el flujo de Ricci en variedades homogeneas". Ph.D. Thesis. Advisor: Jorge Lauret. March 2013.
"Clasificacion de nilradicales Einstein filiformes de dimension 8". Undergraduate thesis (for my Licenciatura degree in Maths). Advisor: Jorge Lauret. March 2008.
"SVD y una Aplicacion a la Transmision de Imagenes" with Julia Yael Plavnik. Monograph for an Applied Math course in 2005.