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Explore the third lecture in a series on geometric models for bounded derived categories of gentle algebras. Delve into the construction of a geometric model that encodes both a marked surface and a line field, providing a complete derived invariant for gentle algebras. Examine how this model extends the Avella-Alaminos and Geiss derived invariant. Discover explicit examples connecting the geometric model to the partially wrapped Fukaya category as described in the work of Haiden, Katzarkov, and Kontsevich. Gain insights into the role of gentle algebras in cluster algebras and homological mirror symmetry, and understand their significance in representing Jacobian algebras of quivers with potentials from triangulated marked surfaces.
