Background
1) Buchweitz, Eisenbud, etc.
2) Orlov’s singularity category and relation to Buchweitz
3) exceptional sequences; relation to tilting and representation theory of quivers; see Bondal, “Helices, representations of quivers, and Koszul algebras” in the volume “Helices and vector bundles” (edited by Rudakov; search the Benson archive for Rudakov to find it).
4) Orlov’s theorem on graded matrix factorizations and their relation to the singularity category
5) Standard resolution of modules over a hypersurface ring - i.e. if R = S/(f) is a hypersurface, this is a functorial way of taking a finite resolution of an R-module M over S and producing a resolution over R. See Eisenbud section 8, and Avramov, Buchweitz, “Homological algebra modulo a regular sequence…” section 2
6) Buchweitz’s Herband difference, Hochster’s theta function: relation to each other, connection to rigidity of Tor vanishing
Dyckerhoff-Murfet
1) Homological perturbation lemma
2) Grothendieck’s residue symbol, local cohomology
3) Dyckerhoff/Murfet I or II
Connections to representation theory
1) Kajiura, Saito, Takahashi - “Matrix factorizations and representations of quivers II”
2) Burban, Iyama, Keller, Reiten
3) Lenzing, de la Pena
Cluster-tilting, non-commutative crepant resolutions
1) basics on cluster tilting
2) Van Den Bergh - “Noncommutative crepant resolutions”
3) Iyama-Wemyss
4) Buchweitz, Leuschke, Van Den Bergh for hypersurfaces
Polishchuk-Vaintrob, Hirzebruch-Riemann-Roch Formula
1) Toen’s homotopy theory for dg-categories
2) Dyckerhoff’s calculation of HH(MF) for an isolated singularity
3) Polishchuk-Vaintrob - HRR paper
Other ideas
1) Aspinwall, Morrsion - “Quivers from matrix factorizations” (on the arxiv)