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Explore the categorification of strata in moduli spaces of quadratic differentials through this 45-minute algebraic geometry lecture. Begin with a comprehensive review of recent developments showing how each stratum can be realized as the space of stability conditions of Fukaya-type triangulated categories, though these categorical realizations are not unique. Delve into the compactification of moduli spaces using categorical methods, examining how category theory provides new tools for understanding these geometric structures. Conclude by investigating the fundamental group structure of strata with simple zeros, discovering its connection to the kernel of the Abel-Jacobi map and uncovering deep relationships between topology and algebraic geometry in this specialized context.
