Lecture notes on quivers with superpotential and their representations

Abstract

These lecture notes are based on a mini-course presented at the fifth version of the Workshop Geometry in Algebra and Algebra in Geometry held in Medellin–Colombia in October 2019. The aim is to provide the background necessary to understand the theory of quivers with relations given by superpotentials. A heavy emphasis is placed throughout on examples to illustrate the applicability of the theory. The motivations for the lectures come from several sources: superpotentials in physics, Calabi–Yau algebras, and noncommutative resolutions.