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
(Heat conduction in harmonic chains of oscillators with alternated masses, in Brazilian Portuguese).



Curriculum vitae                                                  Google Scholar



Research Interests

My 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).

Projects

  • Topological approach to classical and quantum Yang--Mills Theory: a theoretical explanation for electric charge quantisation, without magnetic poles, was obtained (charge quantisation). 


Publications

  1. Romero Solha
    Charge quantisation without magnetic poles: a topological approach to electromagnetism.
    Journal of Geometry and Physics, pages 57--67, volume 99, January 2016. 

  2. Romero Solha
    Circle actions in geometric quantisation.
    Journal of Geometry and Physics, pages 450--460, volume 87, January 2015.

  3. 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.

  4. Eva Miranda and Romero Solha
    On a Poincaré lemma for foliations.
    Foliations 2012, pages 115--137, December 2013.

  5. 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

  1. Eva Miranda, Francisco Presas, and Romero Solha
    Geometric quantisation of almost toric manifolds.
    arXiv:1705.06572.

  2. 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.

 Lecture notes


                                                                                                                                               Last modified: the 4th of August, 2017.