The trimester is devoted to asymptotic properties of infinite and big finite groups, in particular, those associated with random walks on these groups. We hope to have a fruitful collaboration covering probabilistic, analytic, algebraic, and geometrical aspects of this subject area as well as their interplay. The non-exhaustive list of topics we are planning to discuss includes:

• isoperimetric, growth and spectral profiles

• amenability and property (T)

• asymptotics and limit theorems for transition probabilities

• rate of escape and entropy

• boundary actions

• the Poisson boundary

• spaces of harmonic functions

• equidistribution and characterization of invariant sets and measures

• rigidity

• groups acting on trees