Limits of discrete structures (ERC)

Limits of discrete structures.

The main goal of the StrucLim project is the development of a mathematical theory that deals with very large structures using methods from analysis. The project has two major and closely connected compontents. One of them is the study of large networks such as the brain or social networks and the other one is a unified treatment of dynamical systems and higher order Fourier analysis. One of the main achievements is a general limit approach to graphs and operators. The power of this approach was demonstrated by solving open problems for both random graphs and matrices. Another main achievement is a novel way of connecting the theory of dynamical systems with higher order Fourier analysis through methods from probability theory. As a result we solved oped problems in both areas.