# Models and Approximations

In research area C, we will focus on the development and foundation of mathematical models and their approximations that are relevant in the life sciences, physics, chemistry, and engineering. We will rigorously analyse the dynamics of structures and pattern formation in deterministic and stochastic systems. In particular, we aim at understanding the interplay of macroscopic structures with their driving microscopic mechanisms and their respective topological and geometric properties. We will develop analytical and numerical tools to understand, utilise, and control geometry-driven phenomena, also touching upon dynamics and perturbations of geometries. Structural connections between different mathematical concepts will be investigated, such as between solution manifolds of parameterised PDEs and non-linear interpolation, or between different metric, variational, and multi-scale convergence concepts for geometries. In particular, we aim to characterise distinctive geometric properties of mathematical models and their respective approximations.