1. The FCT research project Irregular connections on algebraic curves and quantum field theory (QuantumG).

   You can watch all seminars on The Youtube channel Irregular Singularities and Quantum Field Theory.

   The Conference Irregular Singularities and Quantum Field Theory will take place at the Lisbon University, from 8 to 11 July 2019.

2. The FCT exploratory project 'A mathematical framework for the ODE/IM correspondence'.

1. The ODE/IM correspondence. I have built solutions of the Bethe Ansatz equations from the opers described by Boris Feigin and Edward Frenkel. The results are mainly contained in three papers published in Communications in Mathematical Physics (CMP).  The first paper (with A Raimondo and D Valeri) (arXiv version / PDF version) concerns the case of the Bethe Ansatz for simply-laced Lie algebras which corresponds to opers defined on untwisted affine Kac Moody algebras, the second paper (with A Raimondo and D Valeri) (arXiv version) concerns the Bethe Ansatz for NON-simply-laced (ADE) Lie algebras corresponding to opers defined on twisted affine Kac Moody algebras. In the third paper (with A Raimondo) we studied opers corresponding to higher order sates of the quantum theory (in the simply-laced case)
   For a brief introduction, you can watch my seminar at the Simons Center for Geometry and Physics .
   
2. Painleve equations and anharmonic oscillators. In a recent collaboration with Pieter Roffelsen published on SIGMA, we studied the singularities distribution of rational solutions of the fourth Painleve equation (PIV), by means of the isomonodromic deformation method.  We showed that the singularities are described by an inverse monodromy problem for a quantum anharmonic oscillators of degree two, and classified them by means of the monodromy representation of a class of meromorphic functions introduced by Nevanlinna. Finally, we computed the asymptotic distribution of the singularities of rational solutions of Hermite type: roots condensate on a some curves in the complex plane and, for each curve the real part of the roots is distributed in accordance with the Wigner's semicircle law.
3. In collaboration wtih Daniele De Martino, we solved a model describing the growth-distribution in colonies of E. Coli from their metabolism.  We retrieve two scaling laws relating the mean growth with the standard deviation and the time-response. In particular, we show that suboptimal growth-rates have faster response and therefore colonies with smaller mean growth rate have faster adaptation. Our findings are published in the paper Asymptotic analysis of noisy fitness maximization, applied to metabolism and growth JSTAT 2016 (arXiv version).

For more information here are my Curriculum vitae *** ,  PhD Thesis , Google Scholar profile, arXiv page and ORCID profile.