Senior Lecturer
Overview
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.
Research Interests
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Differential Geometry
I enjoy thinking about problems in Differential Geometry, especially those involving symmetry. These problems are usually connected with many other areas of mathematics which are also of my interest, such as geometric analysis, differential equations, Lie theory, and invariant theory.
Qualifications
- Doctor of Philosophy, Universidad Nacional de Cordoba
Publications
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Journal Article: Hermitian manifolds with flat Gauduchon connections
Lafuente, Ramiro A. and Stanfield, James (2023). Hermitian manifolds with flat Gauduchon connections. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 11. doi: 10.2422/2036-2145.202210_005
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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, 36 (3), 591-651. doi: 10.1090/jams/1022
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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
Grants
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Geometric evolution of spaces with symmetries
(2024–2027) ARC Discovery Projects
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Einstein's equations in the presence of symmetries
(2024) UQ Foundation Research Excellence Awards
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Geometric flows and distinguished geometric structures with symmetry
(2019–2023) ARC Discovery Early Career Researcher Award
Supervision
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Curvature Problems in Hermitian Geometry
(2023) Doctor Philosophy
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Existence and non-existence of Ricci solitons with symmetry
Master Philosophy
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Geodesics on Homogeneous Spaces and connections to the Euler Fluid Equations
Doctor Philosophy
Available Projects
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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.
Publications
Journal Article
-
Hermitian manifolds with flat Gauduchon connections
Lafuente, Ramiro A. and Stanfield, James (2023). Hermitian manifolds with flat Gauduchon connections. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 11. doi: 10.2422/2036-2145.202210_005
-
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, 36 (3), 591-651. 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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Lafuente, R. and Lauret, J. (2014). On homogeneous Ricci solitons. The Quarterly Journal of Mathematics, 65 (2), 399-419. doi: 10.1093/qmath/hat028
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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
Grants (Administered at UQ)
-
Geometric evolution of spaces with symmetries
(2024–2027) ARC Discovery Projects
-
Einstein's equations in the presence of symmetries
(2024) UQ Foundation Research Excellence Awards
-
Geometric flows and distinguished geometric structures with symmetry
(2019–2023) ARC Discovery Early Career Researcher Award
PhD and MPhil Supervision
Current Supervision
-
Existence and non-existence of Ricci solitons with symmetry
Master Philosophy — Principal Advisor
-
Geodesics on Homogeneous Spaces and connections to the Euler Fluid Equations
Doctor Philosophy — Associate Advisor
Other advisors:
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Computational 4-manifold topology
Doctor Philosophy — Associate Advisor
Other advisors:
Completed Supervision
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Curvature Problems in Hermitian Geometry
(2023) Doctor Philosophy — Principal Advisor
Other advisors:
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Arithmetic geometry of character stacks and their E-polynomials
(2022) Master Philosophy — Associate Advisor
Other advisors:
Possible Research Projects
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.
