### Research profiles

Christof Melcher's reseach areas lie in nonlinear partial differential equations, the calculus of variations and applications to specific models in physics and materials science. He is particularly interested in the emergence and dynamics of patterns, microstructures, and topological defects, especially in micromagnetics and Ginzburg-Landau theory. Using tools from mathematical analysis, the goal is to capture qualitative behavior of complex multiscale systems and if possible to identify effective theories that are simpler to understand, to analyze, or to simulate. Results explain, e.g., the internal structure of Neel walls in thin films or give a rigorous derivation of effective equations of motion for magnetic vortices. Specific questions also concern qualitative properties and regularity theory for partial differential equations, particularly geometric evolution equations such as the Landau-Lifshitz equation or elliptic systems with oscillating coefficients. Such questions play a central role in the investigation of singularity formation and blow-up or in homogenization theory. Further topics are spectral methods in numerical analysis, particularly for multiphase evolution problems, and extended Landau-Lifshitz models with spin-transfer interaction, emerging, e.g., in spintronic applications.

Maria G. Westdickenberg's research