The aim of our project is to bring together prominent mathematicians who work in areas related to geometric group theory, measurable group theory, probability and dynamics. More precisely, we have a certain number of themes, which already proved to be rich and fruitful and at the same time promising for future developments, and for which we expect new interactions to lead to important breakthroughs and new perpectives. Theme 1: Actions on metric spaces -- fixed points versus properness. The interactions between a group and the spaces on which it acts lie at the heart of geometric group theory. Concerning isometric actions on metric spaces, their study is structured between two essential and opposite poles : proper actions on the one hand and fixed point properties on the other. The most famous fixed point property, with countless applications, is certainly Kazhdan's Property (T), a definition of which can be formulated as follows: any isometric action on a Hilbert space has a fixed point. On the opposite side, the Haagerup property (existence of a proper isometric action on a Hilbert space) has drawn a lot of attention, notably due to its connection with the Baum-Connes conjecture. These properties can either be extended to more general Banach spaces, yielding strengthenings of Property (T); or specialized, for instance to actions on CAT(0) cube complexes. The relationships between these variants have been the object of many investigations. Despite several breakthrough results, many questions remain open. Theme 2: Topological and measured dynamics of group actions. Over the last decades, there has been a huge amount of work in generalising various aspects of dynamics and ergodic theory from one transformation to the action of a general, often countable, group. Though it might seem surprising at first sight, it appears that the action of a group G on its space of subgroups, denoted Sub(G), simply by conjugacy, plays an important role in dynamics of group actions. This is exemplified by the recent emergence of two notions that proved useful for a variety of questions : the notion of invariant random subgroup, in short IRS, which designates an invariant probability measure on Sub(G), and the notion of uniformly recurrent subgroup, in short URS, which is a minimal closed invariant subset of Sub(G). Further study is undoubtedly needed and constitutes two important objectives in this theme. The third one is the study of random walks on groups. Though this topic originated way earlier, it has been the object of spectacular recent progresses, which call for further developments. Theme 3: Coarse geometry of groups A central branch of geometric group theory is the study of finitely generated groups up to quasi-isometries. We plan to contribute to the classification problem, notably for the class of solvable groups, which remains largely open. But our goal is also to spread the study of coarse properties of groups in other directions. A natural extension of the question of whether two groups are quasi-isometric, is whether a group can ``embed" into another. The type of embeddings that have been mostly studied so far are quasi-isometric embeddings. For instance it is well-known that an amenable group does not quasi-isometrically embed into a hyperbolic group unless it is virtually cyclic. By contrast the more flexible notion of coarse embedding remains much more mysterious. It is however arguably more natural than quasi-isometric embeddings: for instance an injective morphism between finitely generated groups is a coarse embedding but is not quasi-isometric in general. In a different direction, we plan to investigate the relatively recent and quickly growing subject of ``quantitative" measure equivalence, which lies at the intersection of geometric group theory and measure group theory.