The interaction between analytic function spaces and operator theory finds its root in the pioneering work of Beurling, who introduced the Hardy space H2, an analytic representation of ℓ2, in order to characterize the lattice of invariant subspaces of the translation operator. This gives rise to model spaces KΘ = H2 ΘH2, inner functions and outer functions. After his work, a whole theory developed focusing on classical operators on H2, such as multiplication operators (like the shift operator) and their cousins, the Toeplitz (e.g. the backward shift) and Hankel operators, composition operator, embedding operators, etc. Another important set of problems in spaces of analytic functions concerns the geometry of reproducing kernels (interpolation, sampling, uniqueness, zeros, etc.) ….

The aim of this conference is focused on recent progress on Hilbert and Banach spaces of holomorphic functions and the operators acting on them. This meeting is a continuation of a series of conferences organized in recent years in Canada and France: Centre de Recherche de Mathématiques at Montreal CRM (2008), at Fields Institute (2011), CRM (2011) and CRM (2013), CIRM (2019 and 2021), thematic semester at Fields Institute (2022).