Welcome to the Webpage of the Collaborative Research Center 1720!

Our Collaborative Research Center Analysis of Criticality: From Complex Phenomena to Models and Estimates is inspired by challenging phenomena in nature, the sciences and mathematics at criticality. We seek to rigorously analyse and extract the underlying mathematical structures. In order to achieve this in a meaningful way, we particularly focus on three project groups:

• Criticality, irregularity and long-range interactions
• Criticality, asymptotics and scaling limits
• Criticality, ill-posedness and efficient representations

Guiding themes are universality, high-dimensionality, the multiple effects of nonlocality and of taming ill-posedness. We will approach these by combing tools and techniques tailored to these situations such as specifically designed function spaces, the analysis of various types of scattering transforms and renormalization methods.