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During this talk, we will recall the definition of generalized Wron-
skians, and exhibit a sub-family, whose elements are called geometric.
Those geometric generalized Wronskians have two advantages: on the
one hand, they allow global geometric constructions, that we will de-
scribe, and on the other hand, they still allow to detect linear indepen-
dance of holomorphic functions (which is the fundamental property of
generalized Wronskians, known since the work of Roth in the 1950s).
We will then present applications of this construction in hyperbolic-
ity (more precisely in the study of families of entire curves in Fermat
hypersurfaces) and in foliation theory.