# Research areas and reports

The members of the Center for Mathematical Analysis, Geometry, and Dynamical Systems actively collaborate with other Portuguese and foreign researchers. Research activity is documented in the annual **Research Reports**.

Below you find a brief description of the main areas of current (2017) research.

## Differential Equations and Dynamical Systems

- Qualitative theory, nonuniform hyperbolicity, Morse-Smale structures, functional and difference equations, reaction-diffusion equations;
- Geometric mechanics and Hamiltonian systems, integrability of equations of mathematical physics;
- Variational problems and Morse theory, variational methods, general relativity;
- Ergodic theory, topological dynamics, zeta functions;
- Stochastic analysis, Markov processes, particle systems.

## Geometry and Topology

including String Theory and Mathematical-Physics

- Symplectic and Poisson geometry; complex, toric and Kähler geometry; geometric mechanics;
- Non-commutative geometry;
- Algebraic topology; knot theory; algebraic geometry; commutative algebra; Hopf algebras; operator algebras; category theory;
- Quantum field theory and string theory; low dimensional geometry and topology; matrix models; mathematical relativity and black holes; geometric and deformation quantization.