Our Mathematical Physics research is aimed to develop and apply different algebraic and geometric techniques for the study of classical and quantum systems, with special emphasis on their symmetry and integrability properties.
Nowadays, our principal research subjects are the following:
- Classical and quantum (super)integrable Hamiltonian systems on curved spaces.
- Hamiltonian structure and integrability properties of Lotka-Volterra systems.
- Lie-Hamilton systems.
- Spacetime geometry.
- Representation theory of Lie groups and algebras.
- Poisson-Lie groups and quantum groups.
- Lie algebra contractions.
- Quantum deformations of spacetime symmetries.
- Lie bialgebra quantization techniques.
- Non-commutative spacetimes in Quantum Gravity.