# Romero Solha

Currently, I am a Postdoc at the Mathematics Department of UPV-EHU.

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*).

**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

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 29th of October, 2020.*