Currently, I am a Postdoc at the Mathematics Department of PUC-Rio. 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
Research
InterestsMy main interest is on the geometry and topology of Classical Physics (Classical Mechanics, Hydrodynamics, General Relativity, and Yang--Mills Theory) and integrable systems (Symplectic Geometry, Lie--Poisson systems, and Soliton Theory). - Topological approach to classical and quantum Yang--Mills Theory: a theoretical explanation for electric charge quantisation, without magnetic poles, was obtained (
*charge quantisation*).
- 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 Poincare 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.
- Eva Miranda, Francisco Presas, and Romero Solha
Geometric quantisation of almost toric manifolds. arXiv:1705.06572. - Romero Solha
Darboux normal form theorem as an example of Liouville integrability theorem. arXiv:1503.07386.
- Romero Solha
Circle actions and geometric quantisation.*(An extended version of the published article)* arXiv:1301.1220.
- Romero Solha
Gauss--Bonnet theorem for compact and orientable surfaces.*(Contains a proof of this remarkable theorem without using triangulations)*
. Last modified: the 4th of August,
2017 |