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This minisymposium will focus on fundamental and applied aspects of shape analysis. Shape analysis remains one of the key problems to applications ranging from automatic object recognition to the field of biomedical imaging in which datasets typically involve multiple geometric structures with morphological variability. Modern methods are at the intersection of several fields in mathematics that span finite and infinite dimensional geometry, optimal control, optimal transport and statistical data analysis. The objective of the mininisymposium is to bring together researchers covering those multiple aspects to present recent ideas in the field and discuss new directions of interest for the community.