A Geometric Model for the Bounded Derived Category of a Gentle Algebra - Sibylle Schroll Lecture 2

Explore the second 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 and completes the Avella-Alaminos and Geiss derived invariant. Discover the connections between the presented geometric model and the description of partially wrapped Fukaya categories 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 as Jacobian algebras of quivers with potentials obtained from triangulations of marked surfaces.