Research

My main interests lie in several fields of Mathematical Physics: classical r-matrix formulation for integrable systems, Hamiltonian and Lagrangian formulation of integrable hierarchies, differential-difference equations for integrable lattices related to random matrix models, hydrodynamic chains and (skew)-orthogonal polynomials, systems with the (quasi)-Painlevé property.

1. r-matrices in integrable systems (2025) 

 https://doi.org/10.48550/arXiv.2510.22427

2. Iterative polynomial regularisation of PIV-type: Hamiltonian systems and Newton polygons (with G. Filiipuk) (2025) 

https://doi.org/10.48550/arXiv.2510.12378

3. Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric 

approach and birational equivalence (with G. Filiipuk) (2025) 

 https://doi.org/10.48550/arXiv.2506.22896

4. Random matrix ensembles and integrable differential identities (with A. Moro and C. Benassi) (2025)

https://doi.org/10.48550/arXiv.2504.11296

5. Geometric aspects of non-homogeneous 1+0 operators (with A. Rizzo and P. Vergallo) (2025)

https://doi.org/10.48550/arXiv.2503.21917

6. Spaces of initial conditions for quartic Hamiltonian systems of Painlevé and quasi-Painlevé type (with T. Kecker) (2024)

https://doi.org/10.48550/arXiv.2412.17135  

1. Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type (with T.Kecker) 

J. Phys. A: Math. Theor. 58 095202 (2025) 

https://doi.org/10.1088/1751-8121/adb819

2. Lagrangian multi-forms on coadjoint orbits for finite-dimensional integrable systems (with V. Caudrelier and A. A. Singh)

Lett. Math. Phys. 114(1) (2024) 

 https://doi.org/10.48550/arXiv.2506.22896

3. Classification of degenerate non-homogeneous Hamiltonian operators (with P. Vergallo) 

J. Math. Phys. 64(3) (2023)

https://doi.org/10.1063/5.0135134

4. Symmetric matrices and hydrodynamic chains (with A. Moro and C. Benassi) 

Lett. Math. Phys. 111(3) (2021)

https://doi.org/10.1007/s11005-021-01416-y

5. Neutrino and photon lensing by black holes: radiative lens equations and post-Newtonian contributions (with C. Corianò, A. Costantini and L. Delle Rose) 

J. High Eneg. Phys. (2015)

https://doi.org/10.1007/JHEP07(2015)160

Integrable systems, random matrices and applications (2022) 

thesis_dellatti.pdf