In many practical applications, certain processes on lower-dimensional embedded structures, such as interfaces or membranes, play a dominant role. Examples are surfactant transport on moving droplets or bubbles (fluid-fluid interfaces), material surface flow on soap films or cell membranes, as well as displacements of curved membranes, shells and beams. Most of these phenomena can be modelled by partial differential equations on stationary or moving manifolds, like convection-diffusion-type models for surfactant transport or (Navier-)Stokes-type models for surface flow.
Recently, there is an increased interest in the numerical approximation of such problems, which is a challenging task. If the manifold is implicitly represented by zero-level sets, then, e.g., special finite element techniques like TraceFEM and CutFEM have been proposed for the discretization of such PDEs. Other approaches use a surface mesh or the extension of the PDE into a narrow band around the manifold.  For higher-order methods, the accurate approximation of the manifold becomes an important task. In the case of moving manifolds, the spatial discretization changes over time and has to be carefully combined with an appropriate time discretization.
The aim of this minisymposion is to bring together researchers working on different ascpects such as modelling, discretization methods and simulation of practical application in the context of PDEs on manifolds and to present recent developments in that field. Contributions to this minisymposium cover: (1) Derivation of PDE models on manifolds based on physical laws and the well-posedness of such models.  (2) Numerical methods for PDEs on manifolds such as (but not limited to) TraceFEM and CutFEM.  (3) Practical applications of PDEs on manifolds, e.g. in the context of transport phenomena,structure mechanics, surface flows, multi-physics, fluid-structure interaction etc.