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.