Lecture series
- Gunnar Fløystad: Letterplace and co-letterplace ideals from partially ordered sets
slides, exercises
- Graham Leuschke: The homological conjectures
notes, exercises
- Jason McCullough: Graded free resolutions of ideals: the Eisenbud-Goto and Stillman conjectures
notes, exercises
Schedule
Detailed schedule
Literature
Here is a list of suggested preparatory reading.
Texts:
- W. Bruns and J. Herzog: Cohen-Macaulay rings
- D. Eisenbud: Geometry of syzygies (especially chapters 4 and 5)
- I. Peeva: Graded syzygies (especially chapter 1)
Survey papers:
- P. Roberts: Intersection theory and the homological conjectures in commutative algebra, ICM 1990, Kyoto.
- M. Hochster: Homological conjectures, old and new, Illinois J. Math. 51 (2007), no. 1, 151--169.
- J. McCullough and A. Seceleanu: Bounding projective dimension, Commutative algebra, 551--576, Springer, New York, 2013.
- G. Fløystad, J. McCullough and I. Peeva: Three themes of syzygies, Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 3, 415--435.
Some more advanced papers:
- G. Fløystad, B.M. Greve, J. Herzog: Letterplace and co-letterplace ideals of posets, J. Pure Appl. Algebra 221 (2017), no. 5, 1218--1241.
- Y. André: La conjecture du facteur direct, preprint.
- B. Bhatt: On the direct summand conjecture and its derived variant, preprint.
- L. Gruson, R. Lazarsfeld and C. Peskine: On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983), no. 3, 491--506.
- J. McCullough and I. Peeva: Counterexamples to the Eisenbud-Goto regularity conjecture, preprint.
- T. Ananyan and M. Hochster: Small subalgebras of polynomial rings and Stillman's conjecture, preprint.
- T. Ananyan and M. Hochster: Ideals generated by quadratic polynomials, Math. Res. Lett. 19 (2012), no. 1, 233--244.
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