Reading seminar on Cohen-Macaulay modules, Matrix Factorizations, and Orlov's correspondence,

Spring 2014
Wednesday 3:30-4:45, CMU 243

We are trying to collectively type up notes using writelatex. The link is here.

Schedule:
4/16/2014 – 4/30/14: Jim, Shawn and Julia are talking in some order.

 

Winter 2014 
Wednesday 3:30-4:30, Low 112

1/15/14, 1/22/14 Orlov’s survey sections 1-4. Riley Casper

Organizational meeting: Friday, January 10, PDL C-36 3:30pm.

Some references: 

·        Orlov’s papers
“Landau-Ginzburg models, D-branes, and Mirror Symmetry” – notes of a course given by Orlov in 2010
“Derived categories of coherent sheaves and triangulated categories of singularities”, Orlov, 2009
“Triangulated categories of singularities and equivalences between Landau-Ginzburg models” Orlov, 2006

·         Two papers by Burke-Walker:
“MATRIX FACTORIZATIONS OVER PROJECTIVE SCHEMES”, 2012
“Matrix Factorization in Higher Codimension” (particularly, appendix A), 2012

Fall 2013
PDL C-36, Friday 4:30-5:30pm 

Description

This is - in a very rough sense - a continuation of the seminar we started in the Fall of 2012 but then interrupted because a good number of participants left for MSRI. As was decided at the first meeting, we shall try to cover Eisenbud's theorem on Matrix Factorizations and Maximal Cohen-Macaulay modules, Buchweitz - Rickard's theorem on the category of singularities and the stable category of CM modules, and the Orlov's correspondence.

Schedule

10/25/2013, 11/1/13 Eisenbud's theorem (and some necessary preliminaries) - Shawn Baland and Kenneth Chan
11/8/13, 11/15/13 Buchweitz-Rickard Theorem - Jim Stark, notes
11/22/13, 12/6/13 Eisenbud’s theorem revisited – Cody Holdaway

Overview of the Orlov's notes "Landau-Ginzburg models, D-branes, and Mirror Symmetry" Riley Casper (postponed till next quarter)

Some references

·  An extensive collection of references from a workshop in Bielefeld in 2011 is here

·  R.-O. Buchweitz, unpublished notes MAXIMAL COHEN-MACAULAY MODULES AND TATE-COHOMOLOGY OVER GORENSTEIN RINGS

·  G. Leuschke, R. Wiegand, "Cohen-Macaulay Representations", AMS (2012)

·  Y. Yoshino, "Cohen-Macaulay Modules over Cohen-Macaulay Rings", LMS Lecture Note Series 146, CUP (1990)

·  Cody`s notes on Exact and stable categories from last year