Research interests
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.
Articles & Preprints
"Classification of nilpotent almost abelian Lie groups admitting left-invariant complex or symplectic structures" with María L. Barberis, Verónica S. Díaz, Yamile Godoy, Isabel Hernández. Available on arXiv:2406.06819.
"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
"On the signature of the Ricci curvature on nilmanifolds" with Ramiro Lafuente. Transformation groups (2022). https://doi.org/10.1007/s00031-021-09686-5.
"The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups" with Mark Gould & Artem Pulemotov. To appear in Communications in Analysis and Geometry 2022.
"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.
Others monographs
"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.