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Tropical convex hulls of finite sets of points are analogues of usual convex hulls, in the geometry over the tropical semiring ($\mathbb{R} $, min,+). They are also images of polytopes in an affine space over the Puisseux series field, under a non-archimedean valuation into the real numbers. They give rise to a family of cellular resolutions of monomial ideals, which includes hull complexes. This is joint work with Mike Develin.