Interplay between the probability theory and geometric group theory yielded many spectacular results enriching both areas. Asymptotic properties of various models coming from statistical physics and probabilities were connected to the geometry and combinatorics of the underlying discrete algebraic structure (for instance a group, a graph, a group action). The study started with simple random walks and their boundary theory and then extended to other models, such as percolation or the Ising model. Substantial progress was achieved on many different fronts, and several applications to group theoretical problems were found outside of probability. The goal of this program is to gather experts from different areas (ranging from group theory to probability) in order to tackle some important challenges using the cutting-edge techniques that surfaced in recent years.

The program of the semester is structured around one Summer School and two Conferences. Two or three colloquium-style Bernoulli lectures will take place during the semester. In between the conferences, a small number of scientists will be in residence at the CIB, thus providing the opportunity for collaborations between experts in different fields.