SLMath CA Summer School

Singularities in Commutative Algebra Through Cohomological Methods

an SLMath Graduate Summer School

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

Lecture notes

Problem Sets: Macaulay2 Set Problem Set 1

Macaulay2 resources:

Introduction to Macaulay2

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): Uniqueness of 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 3 (Tuesday, July 7)

Lecture 5 (Wednesday, July 8): Deviations (section 1.5)

Lecture 6 (Wednesday, July 8): Graded Lie algebras (sections 3.1 and 3.2)

Lecture 7 (Thursday, July 9): Quadratic models (sections 3.3 and 3.4)

Problem Set 4 (Thursday, July 9)

Lecture 8 (Thursday, July 9): The homotopy Lie algebra of a local ring, and also in M2 (section 3.5)

Problem Set 5 (Thursday, July 9)

Commutative algebra background:

Useful links:

The Official website for our summer school

The Macaulay2 website