Overview
Background
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.
Availability
- Associate Professor Ramiro Lafuente is:
- Available for supervision
Fields of research
Qualifications
- Doctor of Philosophy, Universidad Nacional de Cordoba
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.
Works
Search Professor Ramiro Lafuente’s works on UQ eSpace
2023
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
2023
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
2022
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, 29 (1), 1-15. doi: 10.1007/s00031-021-09686-5
2022
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
2020
Journal Article
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
2019
Journal Article
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
2019
Journal Article
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
2017
Journal Article
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
2017
Journal Article
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
2017
Journal Article
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
2014
Journal Article
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
2014
Journal Article
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
2014
Journal Article
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
2014
Journal Article
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
2014
Journal Article
On homogeneous Ricci solitons
Lafuente, R. and Lauret, J. (2014). On homogeneous Ricci solitons. The Quarterly Journal of Mathematics, 65 (2), 399-419. doi: 10.1093/qmath/hat028
2013
Journal Article
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
Supervision
Availability
- Associate Professor Ramiro Lafuente is:
- Available for supervision
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Available projects
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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.
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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.
Supervision history
Current supervision
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Master Philosophy
Existence and non-existence of Ricci solitons with symmetry
Principal Advisor
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Master Philosophy
Existence and non-existence of expanding Ricci solitons
Principal Advisor
-
Doctor Philosophy
Geometric flows with symmetry
Principal Advisor
Other advisors: Professor Artem Pulemotov
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Doctor Philosophy
A computational approach to 4-manifold topology
Associate Advisor
Other advisors: Professor Benjamin Burton
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Doctor Philosophy
Geodesics on Homogeneous Spaces and connections to the Euler Fluid Equations
Associate Advisor
Other advisors: Professor Artem Pulemotov
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Doctor Philosophy
A computational approach to 4-manifold topology
Associate Advisor
Other advisors: Professor Benjamin Burton
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Doctor Philosophy
Computational 4-manifold topology
Associate Advisor
Other advisors: Professor Benjamin Burton
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Doctor Philosophy
Efficient algorithms in three-dimensional topology
Associate Advisor
Other advisors: Professor Benjamin Burton
Completed supervision
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2023
Doctor Philosophy
Curvature Problems in Hermitian Geometry
Principal Advisor
Other advisors: Professor Artem Pulemotov
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2022
Master Philosophy
Arithmetic geometry of character stacks and their E-polynomials
Associate Advisor
Other advisors: Associate Professor Masoud Kamgarpour
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