EWM-EMS Summer School: Kinetic Theory Arising from Mathematical Biology

Understanding the dynamics of models for biophysical systems is key to fully comprehending them and has attracted the interest of mathematicians for many years. Often, purely deterministic models fail to capture the realistic dynamical behaviour of biological systems due to a certain amount of stochasticity inherent in their evolution. Also, when considering models for a large number of interacting agents, one needs to take into account that each individual is endowed with a specific activity in addition to mechanical variables such as position and velocity. Thus, describing the overall state of the system, in a kinetic framework, by a suitable probability distribution over some microscopic states can ease the analysis and help to reveal new properties. Kinetic theory, and in particular nonlinear kinetic PDEs, have proven to be very powerful, effective and useful tools in mathematical biology in the recent years. Kinetic models have for example been well applied to large systems of interacting agents coming especially from structured population dynamics such as shoals of fish, bacteria, and neurons, and to coagulation-fragmentation processes. 

The aim of the summer school is to introduce younger researchers to applications of well-known analytical methods for studying kinetic models arising from mathematical biology, as well as exploring recent developments within the field.