Introduction to A-Infinity Structures - Bernhard Keller

Dive into the world of A-infinity structures in this comprehensive lecture, the first in a minicourse series. Explore fundamental concepts of A-infinity algebras, their modules, and derived categories. Begin with two motivating problems from representation theory before delving into the topological origins of A-infinity structures. Learn about the definition and study of A-infinity algebras and their morphisms, with a focus on the crucial bar construction and Kadeishvili's theorem on minimal models. Discover the derived category of an A-infinity algebra or category, and examine its full subcategory generated by representables using twisted objects. This 69-minute lecture, presented by Bernhard Keller at the Hausdorff Center for Mathematics, provides a solid foundation for understanding these complex mathematical structures.