Research Area B:

Shape, pattern and partial differential equations

The interplay of the concepts of shape (interfaces in materials or geometric contours in images) and pattern (microstructures in materials or textures in images) characterises mathematical models both in the natural sciences and in computer vision and imaging. This Research Area capitalises on the similarity of the mathematical tools involved: differential geometry, the calculus of variations, and nonlinear partial differential equations. Examples of this fruitful interplay are the rigorous understanding of

  • lower dimensional elasticity theories,
  • multiscale models bridging between statistical physics and continuum mechanics,
  • pattern formation and interface dynamics in biological models, or
  • the combination of Riemannian geometry and continuum mechanics in shape space theory.

Research in this area emphasises the understanding of concrete phenomenons in connection to challenging applications over the development of abstract theory. Furthermore, we aim at developing fast and reliable numerical algorithms in a close interplay with modeling and analysis.

Leaders of the Research Area

Further Investigators