Title: Systems of weakly self-avoiding polygons
Abstract: We consider systems of weakly self-avoiding loops interacting by mutual repulsion. The model depends on a parameter which rewards the total loop length. This model is not only mathematically interesting on its own, but it is also a description of other relevant statistical mechanics models, such as the Spin O(N) model and the double dimer model, and it is related to the Bose gas. The main question is understanding the typical size of the loops in the limit of large boxes and the phase transition phenomenon. This mini-course will provide an overview and present some of the main mathematical techniques, such as reflection positivity.