Publications
Articles and preprints
Homogeneous generalized Ricci flow, with Elia Fusi and James Stanfield.
Preprint (2024).
Non-compact Einstein manifolds with unimodular isometry group, with Christoph Böhm.
Submitted (2023). Slides for a talk about this project.
Ancient Ricci flows of bounded girth, with Theodora Bourni, Tim Buttsworth and Mat Langford.
Preprint (2023).
Hermitian manifolds with flat Gauduchon connections, with James Stanfield.
To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2023).
Non-compact Einstein manifolds with symmetry, with Christoph Böhm.
Journal of the American Mathematical Society 36 n. 3 (2023), 591—651 .
Recordings of a 90min mini-course and a seminar talk on this paper. Slides and video of my plenary talk at DGA 2022.
On the signature of the Ricci curvature on nilmanifolds, with Romina Arroyo.
To appear in Transformation Groups (2021), 12 pages.
Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, with Christoph Böhm.
Geometry & Topology 26 (2022), 899--936. Video of a talk on this paper.
Hermitian curvature flow on Lie groups and static invariant metrics, with Mattia Pujia and Luigi Vezzoni.
Transactions of the American Mathematical Society 373 (2020), 3967—3993.
The Ricci flow on solvmanifolds of real type, with Christoph Böhm.
Advances in Mathematics, vol. 352 (2019), 516-540.
The long-time behavior of the homogeneous pluriclosed flow, with Romina Arroyo.
Proceedings of the London Mathematical Society, (3) 119 (2019), 266–289.
Immortal homogeneous Ricci flows, with Christoph Böhm.
Inventiones Mathematicae, vol. 212 n. 2 (2018), 461–529.
Optimal curvature estimates for homogeneous Ricci flows, with Christoph Böhm and Miles Simon.
International Mathematics Research Notices, vol. 2019 iss. 14 (2019), 4431–4468.
The Alekseevskii conjecture in low dimensions, with Romina Arroyo.
Mathematische Annalen, vol. 367 n. 1 (2017), pp. 283-309.
On homogeneous warped product Einstein metrics
Bulletin of the London Mathematical Society, vol. 47 iss. 1 (2015), pp. 118-126.
Homogeneous Ricci solitons in low dimensions, with Romina Arroyo.
International Mathematics Research Notices, vol. 2015 iss. 13 (2015), pp. 4901-4932.
Scalar curvature behaviour of homogeneous Ricci flows
The Journal of Geometric Analysis, vol. 25 iss. 4 (2015), pp. 2313-2322.
Structure of homogeneous Ricci solitons and the Alekseevskii conjecture, with Jorge Lauret.
Journal of Differential Geometry, vol. 98 n. 2 (2014), pp. 315-347.
On homogeneous Ricci solitons, with Jorge Lauret.
The Quarterly Journal of Mathematics, vol. 65 n. 2 (2014), pp. 399-419.
Solvsolitons associated with graphs
Advances in Geometry, vol. 13 iss. 2 (2013), pp. 255-275.
Follow this link for a list of these articles/preprints on arXiv.
Articles in preparation
The long-time behaviour of collapsed Ricci flows, with Francesco Pediconi.
Book chapters
Real geometric invariant theory (with Christoph Böhm)
In Differential Geometry in the Large (London Mathematical Society Lecture Note Series). Cambridge: Cambridge University Press (2020).
Conference proceedings
Immortal homogeneous Ricci flows
Oberwolfach Reports, 28 (2016), pp. 1595-1597.
The Alekseevskii conjecture in low dimensions
Oberwolfach Reports, 45 (2014), pp. 2565-2566.
A survey on homogeneous Ricci flow
Oberwolfach Reports, 45 (2014), pp. 2541-2543.
Other notes
The following are some notes I wrote as an undergraduate. Most of them are in Spanish.
Solitones de Ricci asociados a grafos, undergraduate thesis (for my Licenciatura degree in Maths), December 2009, pdf.
Teorema de Stokes en variedades (with Joaquin Rodrigues), 1er premio concurso de monografias de la UMA 2009, pdf.
Normas inducidas del multiplicador de Hadamard, monograph for a Matrix Analysis course in 2009, pdf.
Metrizacion, monograph for a Topology course in 2008, pdf.
Los numeros p-adicos y el teorema de Hasse-Minkowski, monograph for an Algebra course in 2007, pdf.
Ejercicios finales de estructuras algebraicas 2007, hand-in exercises for an Algebra course, pdf.
Aplicaciones de la descomposicion en valores singulares, monograph for an Applied Math course in 2006, pdf.