Bridgeland stability conditions relative to a boundary

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In this talk I will present a construction of relative Bridgeland stability conditions that appeared in my work on stability of topological Fukaya categories of surfaces. This construction gives a local-to-global tool for constructing stability conditions. I will explain what technical features of such Fukaya categories render this construction useful in their context, and time allowing discuss the challenges involved in applying these ideas to other contexts such as Bridgeland-Smith type stability conditions and topological Fukaya categories with coefficients.