Dr Andrus Allan Giraldo Munoz

Biography

See my homepage for up-to-date information.

Research | Current

• Global bifurcations theory of vector fields
• Numerical continuation techniques
• Compactification techniques applied to vector fields
• Nonlinear optics
• Semiclassical analysis of quantum optical systems

I am a mathematician specialising in Dynamical Systems. My research focuses on global bifurcations, and the application of state-of-the-art computational techniques for their detection and for understanding their overall behaviour. My research aims to connect theoretical results in the area of dynamical systems with physical phenomena for the purpose of understanding their qualitative behaviour.

Currently, I am studying and characterising dynamical phenomena that arises in different optical devices, e.g., photonic crystal nanocavities, fibre ring resonators; and in the semiclassical approximation of different quantum optical models. 

Additionally, I am also developing and applying novel formulations for the continuation of two-point boundary value problems in the pursue of connecting known results in ODEs to PDEs, and delay differential equations.

Teaching | Current

MATHS 765: Mathematical Modelling -- Semester 2, 2021