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Delve into the second lecture of Bernhard Keller's minicourse on A-infinity structures, presented at the Winter School JTP by the Hausdorff Center for Mathematics. Explore advanced concepts in A-infinity algebras, their modules, and derived categories over the course of 1 hour and 14 minutes. Build upon the foundation laid in the first lecture by examining two motivating problems from representation theory and briefly investigating the topological origins of A-infinity structures. Learn the definitions and properties of A-infinity algebras and their morphisms, with a focus on the crucial bar construction and Kadeishvili's theorem on minimal models. Conclude by studying the derived category of an A-infinity algebra or category, and discover how to describe its full subcategory generated by representables using twisted objects.
