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Explore the first lecture in a series on geometric models for the bounded derived category of gentle algebras. Delve into the significance of gentle algebras in various mathematical fields, including cluster algebras and homological mirror symmetry. Learn about their role as Jacobian algebras in quivers with potentials derived from triangulations of marked surfaces, and their appearance in the construction of partially wrapped Fukaya categories. Discover how gentle algebras encode both a marked surface and a line field, leading to a complete derived invariant that expands upon the work of Avella-Alaminos and Geiss. Examine concrete examples connecting the introduced geometric model to the description of partially wrapped Fukaya categories as presented in the research of Haiden, Katzarkov, and Kontsevich.
