Introduction to A-infinity structures 2

Introduction to A-infinity structures 2

In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we 
will briefly present the topological origin of A-infinity structures. We will then define and study A-infinity algebras and their morphisms. Of central importance are the bar construction and Kadeishvili's theorem on the existence of minimal models. We will then define the derived category of an A-infinity algebra or category and describe its full subcategory generated by the representables using twisted objects.

NOTA: Esta charla es parte de la Escuela de Invierno "Connections between representation theory and geometry" que del 5 al 23 de octubre de 2020 tendrá lugar virtualmente en el Hausdorff Research Institute for Mathematics (HIM) de Bonn, Alemania, organizada por Jenny August, Sondre Kvamme, Daniel Labardini-Fragoso y Alexandra Zvonareva. Si quieres asistir, por favor visita la página web de la Escuela de Invierno e inscríbete.