The research lines active within the PhD programme in Mathematics and Applications:

- Harmonic and functional analysis
- Mathematical logic and category theory
- Commutative algebra and computer algebra
- Complex projective geometry
- Analytic number theory
- Arithmetic geometry and algebraic number theory
- Geometrical methods in physical theories
- Mathematical aspects of quantum mechanics and algebraic quantum field theory
- Probability and mathematical statistics
- Numerical analysis and computational methods with applications in medical imaging, neurosciences and astrophysics