Compactifications of spaces of Landau–Ginzburg models

This paper reviews the results and techniques from the authors' work on Landau–Ginzburg degenerations and applies them in basic examples. The main example is the $A_n$-category, where we observe a relationship to stability conditions and directed quiver representations. We conclude with a brief survey of applications to the birational geometry of del Pezzo surfaces.
Bibliography: 31 titles.