ZIH-Colloquium - "Attraction and Repulsion in Biological Tissues: Challenges for Mathematical ..."

"Attraction and Repulsion in Biological Tissues: Challenges for Mathematical Models, Analysis, and Numerics"
Cell attraction and repulsion are essential processes in biological tissues. Cellular adhesion, in particular, plays a key role during embryonic development and in the invasion of healthy tissues by tumour cells. In this talk, after an introduction to the biological motivation, I present a non-local partial differential equation model of attraction and repulsion which goes back to work by Armstrong, Painter, and Sherratt (2006). This is followed by a recent derivation of this model from an individual-based model, an overview of analytical results, and an identification of numerical challenges with respect to the treatment of nonlocal terms and their resolution. Finally, I will give a glance on current work regarding adhesion on growing domains.
Alf Gerisch is a researcher in the Numerical Analysis and Scientific Computing group at Technische Universität Darmstadt. He received his Master's degree in Mathematics from the University of Dundee (Scotland, UK) and his doctoral degree (Dr. rer. nat.) from Martin-Luther-Universität Halle-Wittenberg. His research is focussed on providing numerical and computational tools for problems from mathematical biology. This includes multiscale models and homogenization techniques for elastic properties of hard tissues and accurate and efficient schemes for the time-dependent simulation of different processes in soft tissues.