In this talk we will work with three, very different, probabilistic objects: the Abelian sandpile model, the Gaussian free field and the uniform spanning tree. The first one is a Markov chain on the integers, the second is an example of a three-dimensional surface, the last one is a type of graph. What do they have in common? We will explain that there is a lens through which you can study them together, and in fact write some observables of the first model as a function of the last two. This lens is represented by a new type of calculus, called "fermionic calculus". Based on joint works with L. Chiarini, R. S. Hazra, A. Rapoport, W. Ruszel.