Professor Peter Markowich’s research is in Applied Mathematics, in particular in the partial differential equations (PDE) which arise in applications. Mine is an ‘integrated’ approach, involving mathematical
analysis, numerical analysis, computational mathematics and mathematical modeling. He has
spent a significant part of my career working on PDE in physics but about ten years ago he switched his research emphasis to PDE applications in the life, social and data sciences, emphasizing both direct and inverse (data assimilation) problems. This change of research direction shall support and help to shape the current trend in modern mathematics of penetrating and becoming indispensable tools also for non-physical data-rich applied sciences. He has been working on recently: inpainting in mathematical imaging, price formation of economical assets, human crowd motion modeling by fluid and mean-field game approaches, large data assimilation in the Navier-Stokes fluid equations, and network formation and adaptation in the biological and social sciences.