SLMath CA Summer School
Singularities in Commutative Algebra Through Cohomological Methods
July 6 through July 17, 2026
Official website
for our summer school
Organizers/Lecturers: Benjamin Briggs, Eloísa Grifo, and Josh Pollitz
TAs: Maya Banks and Ryan Watson
Main resources:
Lecture notes
Problem Sets: Macaulay2 Set
Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
Macaulay2 resources:
Introduction to Macaulay2
Minimal models
Homotopy Lie algebra
Teams for week 1
Teams for week 2
Plan
Lecture 1 (Monday, July 6):
free resolutions and the Koszul complex (chapter 0 and section 1.1)
Introduction to Macaulay2 (Monday, July 6):
an interactive session
Lecture 2 (Monday, July 6):
dg algebras and adjoining variables to kill cycles (sections 1.2 and 1.3)
Problem Set 1 (Monday, July 6)
Lecture 3 (Tuesday, July 7):
Minimal models (section 1.3) and minimal models in M2
Problem Set 2 (Tuesday, July 7)
Lecture 4 (Tuesday, July 7): Complete intersections (section 1.4)
Problem Set 2 (Tuesday, July 7)
Lecture 5 (Wednesday, July 8): Deviations (section 1.5)
Lecture 6 (Wednesday, July 8): Graded Lie algebras (sections 2.1 and 2.2)
Lecture 7 (Thursday, July 9): Quadratic models (sections 2.2 through 2.4)
Problem Set 3 (Thursday, July 9)
Lecture 8 (Thursday, July 9): The homotopy Lie algebra of a local ring, and also in M2 (section 2.5)
Problem Set 3 (Thursday, July 9)
Lecture 9 (Friday, July 10): DG modules (section 3.1)
Problem Set 4 (Friday, July 10)
Lecture 10 (Friday, July 10): DG modules (section 3.1)
Problem Set 4 (Friday, July 10)
Lecture 11 (Monday, July 13): Previously, on...
Problem Set 5 (Monday, July 13)
Lecture 12 (Monday, July 13): Derivations (section 4.2)
Problem Set 6 (Monday, July 13)
Lecture 13 (Tuesday, July 14): Towards a proof of Vasconcelos' Conjecture (section 4.3)
Problem Set 7 (Tuesday, July 14)
Lecture 14 (Tuesday, July 14): Vasconcelos' Conjecture (section 4.3)
Problem Set 7 (Tuesday, July 14)
Lecture 15 (Wednesday, July 15): A brief introduction to derived categories
Lecture 16 (Wednesday, July 15): Resolutions over hypersurfaces (section 5.1)
Lecture 17 (Thursday, July 16): Cohomological support varieties (section 5.2)
Problem Set 8 (Thursday, July 16)
Lecture 17 (Thursday, July 16): Cohomological support varieties detect the ci property (section 5.3)
Problem Set 8 (Thursday, July 16)
Lecture 19 (Friday, July 17): Avramov-Halperin through cohomological support varieties
Lecture 20 (Friday, July 17): A characterization of cis via the derived category
Lecture 21 (Friday, July 17): Embedded deformations
Other resources
Commutative algebra background:
Commutative algebra
Commutative algebra II
Homological algebra
Useful links:
The Official website for our summer school
The Simons Laufer Mathematical Sciences Institute
The Macaulay2 website
Avramov's Infinite free resolutions
Jack Jeffries' notes on classical Kähler differentials