I was born in Argentina and found an early passion for mathematics as a high school student by participating in the Math and Programming Olympiads. I obtained an undergraduate degree from La Plata University in 2009, and a PhD in mathematics from Cordoba University under the supervision of Prof. Jorge Lauret in 2013. After that I was a postdoc in the Differential Geometry group at the University of Münster in Germany (first as a Humboldt fellow, and then as Prof. Wilking's assistant). I also spent three months at MSRI in Berkeley, California during 2016. Since mid 2018, I am a Lecturer at the School of Maths and Physics in UQ.
Journal Article: Non-compact Einstein manifolds with symmetry
Böhm, Christoph and Lafuente, Ramiro A. (2023). Non-compact Einstein manifolds with symmetry. Journal of the American Mathematical Society. doi: 10.1090/jams/1022
Journal Article: On the signature of the Ricci curvature on nilmanifolds
Arroyo, Romina M. and Lafuente, Ramiro A. (2022). On the signature of the Ricci curvature on nilmanifolds. Transformation Groups, 1-15. doi: 10.1007/s00031-021-09686-5
Journal Article: Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
Boehm, Christoph and Lafuente, Ramiro A. (2022). Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds. Geometry and Topology, 26 (2), 899-936. doi: 10.2140/gt.2022.26.899
Geometric flows and distinguished geometric structures with symmetry
(2019–2022) ARC Discovery Early Career Researcher Award
Existence and non-existence of Ricci solitons with symmetry
Master Philosophy
Hermitian Curvature Flows With Symmetries
Doctor Philosophy
Arithmetic geometry of character stacks and their E-polynomials
(2022) Master Philosophy
Riemannian geometry with symmetries
Despite the field's long history, many important questions in Riemannian geometry involving symmetry assumptions remain open to this day. An example is the long-standing Alexeevskii conjecture (1970's) on homogeneous Einstein spaces. With new tools having been developed in recent years by the supervisor and his collaborators, among others, this is an inviting time to tackle some of these problems.
Geometric flows in Hermitian geometry
There are a number of challenging projects being offered in the area of complex geometry, with an emphasis in geometric evolution equations with symmetries. With the aim of generalising the Ricci flow to Hermitian, non-Kaehler geometries, these evolution equations have gained significant interest in recent years, and most basic questions about them are still unanswered.
Non-compact Einstein manifolds with symmetry
Böhm, Christoph and Lafuente, Ramiro A. (2023). Non-compact Einstein manifolds with symmetry. Journal of the American Mathematical Society. doi: 10.1090/jams/1022
On the signature of the Ricci curvature on nilmanifolds
Arroyo, Romina M. and Lafuente, Ramiro A. (2022). On the signature of the Ricci curvature on nilmanifolds. Transformation Groups, 1-15. doi: 10.1007/s00031-021-09686-5
Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
Boehm, Christoph and Lafuente, Ramiro A. (2022). Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds. Geometry and Topology, 26 (2), 899-936. doi: 10.2140/gt.2022.26.899
Hermitian curvature flow on unimodular Lie groups and static invariant metrics
Lafuente, Ramiro A., Pujia, Mattia and Vezzoni, Luigi (2020). Hermitian curvature flow on unimodular Lie groups and static invariant metrics. Transactions of the American Mathematical Society, 373 (6), 3967-3993. doi: 10.1090/tran/8068
The Ricci flow on solvmanifolds of real type
Böhm, Christoph and Lafuente, Ramiro A. (2019). The Ricci flow on solvmanifolds of real type. Advances in Mathematics, 352, 516-540. doi: 10.1016/j.aim.2019.06.014
The long-time behavior of the homogeneous pluriclosed flow
Arroyo, Romina M. and Lafuente, Ramiro A. (2019). The long-time behavior of the homogeneous pluriclosed flow. Proceedings of the London Mathematical Society, 119 (1), 266-289. doi: 10.1112/plms.12228
Optimal curvature estimates for homogeneous Ricci flows
Böhm, Christoph, Lafuente, Ramiro and Simon, Miles (2017). Optimal curvature estimates for homogeneous Ricci flows. International Mathematics Research Notices, 2019 (14), 4431-4468. doi: 10.1093/imrn/rnx256
Immortal homogeneous Ricci flows
Böhm, Christoph and Lafuente, Ramiro A. (2017). Immortal homogeneous Ricci flows. Inventiones mathematicae, 212 (2), 461-529. doi: 10.1007/s00222-017-0771-z
The Alekseevskii conjecture in low dimensions
Arroyo, Romina M. and Lafuente, Ramiro A. (2017). The Alekseevskii conjecture in low dimensions. Mathematische Annalen, 367 (1-2), 283-309. doi: 10.1007/s00208-016-1386-1
On homogeneous warped product Einstein metrics
Lafuente, Ramiro A. (2014). On homogeneous warped product Einstein metrics. Bulletin of the London Mathematical Society, 47 (1), 118-126. doi: 10.1112/blms/bdu103
Structure of homogeneous Ricci solitons and the Alekseevskii conjecture
Lafuente, Ramiro and Lauret, Jorge (2014). Structure of homogeneous Ricci solitons and the Alekseevskii conjecture. Journal of Differential Geometry, 98 (2), 315-347. doi: 10.4310/jdg/1406552252
Scalar Curvature Behavior of Homogeneous Ricci Flows
Lafuente, Ramiro A. (2014). Scalar Curvature Behavior of Homogeneous Ricci Flows. The Journal of Geometric Analysis, 25 (4), 2313-2322. doi: 10.1007/s12220-014-9514-1
Homogeneous Ricci solitons in low dimensions
Arroyo, Romina M. and Lafuente, Ramiro (2014). Homogeneous Ricci solitons in low dimensions. International Mathematics Research Notices, 2015 (13), 4901-4932. doi: 10.1093/imrn/rnu088
Lafuente, R. and Lauret, J. (2014). On homogeneous Ricci solitons. The Quarterly Journal of Mathematics, 65 (2), 399-419. doi: 10.1093/qmath/hat028
Solvsolitons associated with graphs
Lafuente, Ramiro A. (2013). Solvsolitons associated with graphs. Advances in Geometry, 13 (2), 255-275. doi: 10.1515/advgeom-2012-0032
Geometric flows and distinguished geometric structures with symmetry
(2019–2022) ARC Discovery Early Career Researcher Award
Existence and non-existence of Ricci solitons with symmetry
Master Philosophy — Principal Advisor
Other advisors:
Hermitian Curvature Flows With Symmetries
Doctor Philosophy — Principal Advisor
Other advisors:
Computational 4-manifold topology
Doctor Philosophy — Associate Advisor
Other advisors:
Arithmetic geometry of character stacks and their E-polynomials
(2022) Master Philosophy — Associate Advisor
Other advisors:
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Riemannian geometry with symmetries
Despite the field's long history, many important questions in Riemannian geometry involving symmetry assumptions remain open to this day. An example is the long-standing Alexeevskii conjecture (1970's) on homogeneous Einstein spaces. With new tools having been developed in recent years by the supervisor and his collaborators, among others, this is an inviting time to tackle some of these problems.
Geometric flows in Hermitian geometry
There are a number of challenging projects being offered in the area of complex geometry, with an emphasis in geometric evolution equations with symmetries. With the aim of generalising the Ricci flow to Hermitian, non-Kaehler geometries, these evolution equations have gained significant interest in recent years, and most basic questions about them are still unanswered.