Introduction to A-Infinity Structures - Bernhard Keller

Explore advanced concepts in A-infinity structures in this third lecture of the Winter School JTP series by Bernhard Keller. Delve into the fundamental aspects of A-infinity algebras, their modules, and derived categories. Begin with two motivating problems from representation theory before examining the topological origins of A-infinity structures. Learn about the definition and properties of A-infinity algebras and their morphisms, with a focus on the crucial bar construction and Kadeishvili's theorem on minimal models. Investigate the derived category of A-infinity algebras and categories, and discover how to describe its full subcategory generated by representables using twisted objects. This one-hour lecture, presented by the Hausdorff Center for Mathematics, offers a comprehensive exploration of these complex mathematical concepts for advanced students and researchers in the field.