The heart fan is a new convex-geometric invariant of an abelian category which captures interesting aspects of the related homological algebra. I will review the construction and some of its key properties, illustrating them through examples. In particular I will explain how the heart fan can be viewed as auniversal phase diagram' for Bridgeland stability conditions with the given heart. This is joint work with Nathan Broomhead, David Pauksztello and David Ploog (arXiv:2310.02844v2).
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