Group: Mathematical models in economics and natural sciences

My scientific work focuses on nonlinear partial differential equations and numerical simulations, with particular emphasis on the analysis of pattern-forming geometric equations such as minimal surfaces and the Helfrich equations coupled with other pattern forming systems.

I am a co-developer of pde2path- a MATLAB package for continuation and bifurcation analysis in systems of PDEs. Currently, my primary focus is on the further development of the Xcont extension, which is designed for the treatment of geometric PDEs. In this context, I employ analytical methods including

• bifurcation theory and multiple scale analysis (e.g., amplitude equations),
• centre manifold reduction,

• numerical continuation and bifurcation detection.