Preface; 1. Topological field theory of data: mining data beyond complex networks? Mario Rasetti and Emanuela Merelli; 2. A random walk in diffusion phenomena and statistical mechanics Elena Agliari; 3. Legendre structures in statistical mechanics for ordered and disordered systems Francesco Guerra; 4. Extrema of log-correlated random variables: principles and examples Louis-Pierre Arguin; 5. Scaling limits, Brownian loops and conformal fields Federico Camia; 6. The Brownian web, the Brownian net, and their universality Emmanuel Schertzer, Rongfeng Sun and Jan M. Swart; Index.