A typical feature of systems at criticality consists of the complex coupling of multiple scales. In many settings, this involves a whole cascade of scales bridging several orders of magnitude. For instance, such cascades may range from atomistic to mesoscopic or macroscopic lengths. Often, this multiscale setting is further accompanied by the interaction of different processes and phenomena. A crucial ingredient in the analysis of such systems is the identification of the leading order contributions by investigating asymptotic regimes and scaling limits. This allows us to isolate the key effects and to study their impact rigorously.

The projects in this research area are

• B01 - Random growth and strongly correlated systems (Ferrari)
• B02 - Optimal design of curved folding structures in thin shells (Conti, Rumpf)
• B03 - Geometry and materials: rigidity, flexibility and scaling in some problems from materials science (Müller, Rüland)
• B04 - Numerical homogenization of multiscale problems with coupled scales (Verfürth)
• B05 - Convergence acceleration by non-reversibility and degenerate noise (Eberle)
• B06 - Kinetic models in inhomogeneous settings (Niethammer, Velázquez)
• B07 - Avoiding critical slowing down in lattice methods by means of tensor methods (Dölz, Griebel)
• B08 - Random matrices and anticoncentration (Sauermann)