Research Activities

Research Unit:

Centre for Mathematics of the University of Coimbra - (research group:  Geometry and applications)

Publications:

  1. Caseiro, R., Françoise, J. P., & Sasaki, R. (2000). Algebraic linearization of dynamics of Calogero type for any Coxeter group. Journal of Mathematical Physics, 41(7), 4679-4686. .
  2. Caseiro, R., Françoise, J. P., & Sasaki, R. (2001). Quadratic algebra associated with rational Calogero-Moser models. Journal of Mathematical Physics, 42(11), 5329-5340.
  3. Caseiro, R., & Françoise, J. P. (2001). Algebraic linearization of hyperbolic Ruijsenaars–Schneider systems. Journal of Nonlinear Mathematical Physics, 8(sup1), 58-61.
  4. Caseiro R. (2002), Master integrals, superintegrability and quadratic algebras. Bulletin des Sciences Mathématiques, 126 (8): 617-630.
  5. Caseiro, R., & Françoise, J. P. (2002). Algebraically linearizable dynamical systems.  In The J. A. Pereira da Silva Birthday Schrift, Textos de Matemática, Série B, 32, Departamento de Matemática da Universidade de Coimbra.
  6. Caseiro, R., & Nunes da Costa, J. (2006). Integrable Systems and Recursion Operators on Symplectic and Jacobi Manifolds, in Encyclopedia of Mathematical Physics,Jean-Pierre Françoise, Gregory L. Naber and Tsou Sheung Tsun (eds.), Oxford Academic Press, Elsevier, volume III, 87-93.
  7. Caseiro, R. (2007). Modular classes of Poisson–Nijenhuis Lie algebroids. Letters in Mathematical Physics, 80(3), 223-238.
  8. Caseiro, R., & Da Costa, J. M. N. (2007). Jacobi–Nijenhuis algebroids and their modular classes. Journal of Physics A: Mathematical and Theoretical, 40(44), 13311.
  9. Caseiro, R. (2008, June). The Modular class of a twisted Jacobi algebroid. In AIP Conference Proceedings (Vol. 1023, No. 1, pp. 71-80). American Institute of Physics.
  10. Caseiro, R., De Nicola, A., & da Costa, J. M. N. (2010). On Jacobi quasi-Nijenhuis algebroids and Courant–Jacobi algebroid morphisms. Journal of Geometry and Physics, 60(6-8), 951-961.
  11. Caseiro, R., & Fernandes, R. L. (2013). The modular class of a Poisson map. In Annales de l'Institut Fourier, Vol. 63, No. 4, pp. 1285-1329.
  12. Caseiro, R., Françoise, J. P., & Sasaki, R. (2013). Inversion of a mapping associated with the Aomoto–Forrester system. Reviews in Mathematical Physics, 25(10), 1343009.
  13. Caseiro, R. (2013). The modular class of a Lie algebroid comorphism. Reviews in Mathematical Physics, 25(10), 1343001.
  14. Caseiro, R. (2016). The modular class of a Dirac map. Journal of Geometry and Physics, 104, 19-29.
  15. Caseiro, R., Vicente, M. F., & Vitória, J. (2019). Projection method and the distance between two linear varieties. Linear Algebra and its Applications, 563, 446-460.
  16. Caseiro, R., Vicente, M. F., & Vitória, J. (2021). Projection of a point onto the intersection of spheres in linear varieties. Linear Algebra and its Applications, 610, 40-51.
  17. Caseiro, R., & Nunes da Costa, J. (2022). $O$-Operators on Lie $\infty$-algebras with respect to Lie $\infty$-actions. Communications in Algebra, 50(7): 3079-3101.
  18. Caseiro, R., & Laurent-Gengoux, C. (2022). Modular class of Lie $\infty$ algebroids and adjoint representations. Journal of Geometric Mechanics, 14 (2):272-305.
  19. Caseiro, R. & Nunes da Costa, J. (2023). Embedding tensors on Lie $\infty$-algebras with respect to Lie $\infty$-actions. Communications in Algebra, 52 (4), 1432-1456.
  20. Caseiro, R. & Petalidou, F. Modular class of Loday algebroids. In preparation.

Preprints: 

  1. Caseiro, R., De Nicola, A., & Da Costa, J. M. N. (2008). On Poisson quasi-Nijenhuis Lie algebroids.  ArXiv:0806.2467.


Theses:

  • Integrabilidade clássica e quântica: uma abordagem algébrica, Doctoral thesis, Universidade de Coimbra, 2003.
  • Variedades bihamiltonianas e de Poisson-Nijenhuis. Redução e aplicações, Master's thesis, Universidade de Coimbra,  1998.

Organized Conferences: