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Explore the intricate connections between symplectic topology, stability conditions, and quadratic differentials in this comprehensive lecture. Delve into the world of symplectic Calabi-Yau manifolds and their associated Fukaya categories, examining how the symplectic mapping class group influences stability conditions. Discover the challenges of computation in this field and learn how this approach has become a powerful tool for studying symplectic mapping class groups. Investigate a fascinating class of examples linked to punctured Riemann surfaces, revealing profound connections between spaces of quadratic differentials in Teichmueller theory and dynamics, and the homological algebra of triangulated categories. Gain insights into this complex subject matter, drawing from the speaker's collaborative work with Tom Bridgeland.
