The goal of this reading group is to cover the first part of the book "Combinatorial Commutative Algebra" by Bernd Sturmfels and Ezra Miller.
Members of the reading group: AJ Greene, Dinesh Limbu, Olalekan Ogunmefun, Matthew Booth.
The goal of this reading group is to cover the first part of the book "Combinatorial Commutative Algebra" by Bernd Sturmfels and Ezra Miller.
Members of the reading group: AJ Greene, Dinesh Limbu, Olalekan Ogunmefun, Matthew Booth.
Meeting 1: 23 Jan 2026, In this meeting, we learned how to write monomials as the intersection of monomial primes, we defined simplex and square-free monomial ideal, and saw the correspondence between them, via Stanley Reisner ideal. We also computed the Stanley-Reisner ideals for some small simplices. (Sections 1.1 and 1.2)
Meeting 2: 30 Jan 2026, In this meeting we reviewd the Homology and its dual for the simplicial complex, and computed some example. (Section 1.3)
Meeting 3: 6 Feb 2026, In this meeting we went over the multigraded Hilebert sereis for monomial ideals and h-polynomials.
Meeting 4: 13 Feb 2026, In this meeting we talked about minimal matrix and saw some explicit combinotarial construction for the Koszul Complex.