Mathematics of Planet Earth

This four month programme shall advance the mathematical modelling and analysis of complex fluids and active media in situations involving interface and contact line dynamics. It is focused on confined systems involving various kinds of interfaces as, for instance, moving or evaporating drops on substrates, vesicles, thin films, crawling and swimming cells, biological membranes and tissues. Dynamical processes of interest to the programme include as well surface induced phase transitions, cell adhesion and locomotion on surfaces, and bio-convection caused by active swimmers interacting with boundaries. The involved complex behaviour is marked by the interplay of different instabilities triggering hierarchical structure formation processes. Theoretical approaches range from stochastic discrete descriptions of processes on the nanoscale to deterministic continuum descriptions of processes on the micro- or macroscopic scales. The latter naturally connect to advances in the analysis of partial differential equations for kinetic theory. Some attention will as well be paid to multiscale analysis and computations.

The programme shall foster the development of advanced mathematical descriptions of the coupling of the bulk dynamics of complex fluids and active media with the dynamics of free surfaces, interfaces and contact lines. Thereby the programme will initiate new collaborations between applied mathematicians and the different communities of physicists or engineers involved in biological physics, soft condensed matter science, chemical/mechanical engineering, nano- and microfluidics, and related fields. The programme combines research seminars, embedded workshops and a summer school with a number of short instructional courses. The latter will particularly allow younger researchers to better integrate concepts of mathematical modelling and non-equilibrium, nonlinear, and soft matter science into the presently active research fields.