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My last postdoctoral research position was at the Department of Geometry and Topology of UGR (Spain).
Previously I have completed postdoctoral research stays at the Department of Mathematics of UPV/EHU (Spain), Department of Mathematics of PUC-Rio (Brazil), Department of Mathematics of UFMG (Brazil), and Centre de Recerca Matemàtica (Spain).
My thesis advisor was Eva Miranda (Universitat Politècnica de Catalunya - UPC).
The Ph.D. thesis deals with geometric quantisation of integrable systems with singularities.
I also hold a master's degree on Physics from UFMG - Universidade Federal de Minas Gerais. My Master's thesis advisor was Emmanuel Araújo Pereira. We studied the nonequilibrium statistical mechanics properties of hamiltonian microscopic models with stochastic dynamics (Heat conduction in harmonic chains of oscillators with alternated masses, in Brazilian Portuguese).
(Adelaide, 2015)
Research Interests
Research Interests
My main interest is on the geometry and topology of Classical Physics (Classical Mechanics, Electromagnetism, General Relativity, and Hydrodynamics) and integrable systems (Symplectic Geometry and Lie--Poisson systems).
Projects
Topological approach to classical and quantum Yang--Mills Theory: a theoretical explanation for electric charge quantisation, without magnetic poles, was obtained (charge quantisation).
Symplectic geometric approach to general relativity: a symplectic structure was obtained (SGGH) for certain oriented 4-dimensional globally hyperbolic lorentzian manifolds, and Schwarzschild's solution is an example (SGSS).
Publications
Publications
Eva Miranda, Francisco Presas, and Romero Solha
Geometric quantisation of almost toric manifolds.
Journal of Symplectic Geometry, pages 1147--1168, volume 18, issue 4, October 2020.Romero Solha
Charge quantisation without magnetic poles: a topological approach to electromagnetism.
Journal of Geometry and Physics, pages 57--67, volume 99, January 2016.Romero Solha
Circle actions in geometric quantisation.
Journal of Geometry and Physics, pages 450--460, volume 87, January 2015.Eva Miranda and Romero Solha
A Poincaré lemma in Geometric Quantisation.
The Journal of Geometric Mechanics, pages 473--491, volume 5, issue 4, December 2013.Eva Miranda and Romero Solha
On a Poincaré lemma for foliations.
Foliations 2012, pages 115--137, December 2013.Emmanuel Pereira and Romero Solha
Some properties of the thermal conductivity of chains of oscillators.
Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, volume 81, pages 062--101, June 2010.
Preprints
Romero Solha
On a symplectic structure for globally hyperbolic spacetimes.Romero Solha
Symplectic geometric aspects of the Schwarzschild solution.
arXiv:2507.02895.Romero Solha
(Attempt on the) Positiveness of mass: a topological approach to newtonian gravity.
Symplectic foliations induced by harmonic forms on 3-manifolds.
arXiv:2108.02012.Romero Solha
Gauss--Bonnet theorem for compact and orientable surfaces: a proof without using triangulations.
arXiv:1709.09040.Romero Solha
Darboux normal form theorem as an example of Liouville integrability theorem.
arXiv:1503.07386.
Last modified: the 20th of June, 2025.
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