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This workshop intends to be a first meeting point for specialists and young researchers active in non-commutative geometry, free probability, and topological recursion. In the two first areas, one often wants to compute expectation values of a large class of non-commutative observables in random ensembles of (several) matrices of size N, in the large N limit. The motivations come from the study of various models of 2d quantum gravity via random spectral triples, or from the problem of identifying of interesting factors via approximations by matrix models. Topological recursion and its generalizations provide a priori universal recipes to make and compactly organize such computations, not only for the leading order in N, but also to all orders of expansion in 1/N.in such a way that bridges to other domains where topological recursion has been applied (like enumerative geometry, tropical geometry, mirror symmetry, topological and more generally low-dimensional quantum field theories) become clear.