1 Background In our report on the first “Derived Category Methods in Commutative Algebra”
workshop (2008) we wrote:“Derived category methods have proved to be very successful in …

We study the asymptotic behavior of the ideals of minors in minimal free resolutions over
local rings. In particular, we prove that such ideals are eventually 2-periodic over complete …

We exhibit an example of a product of two proper monomial ideals such that the residue
class ring is not Golod. We also discuss the strongly Golod property for rational powers of …

We define a notion of compressed local Artinian ring that does not require the ring to contain
a field. Let (R, m) be a compressed local Artinian ring with odd top socle degree s, at least …

Supersolvable hyperplane arrangements and matroids are known to give rise to certain
Koszul algebras, namely their Orlik-Solomon algebras and graded Varchenko-Gel'fand …

Three themes of syzygies Page 1 BULLETIN (New Series) OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 53, Number 3, July 2016, Pages 415–435 http://dx.doi.org/10.1090/bull/1533 …

The Taylor resolution is a fundamental object in the study of free resolutions over the
polynomial ring, due to its explicit formula, cellular/combinatorial structure, and applicability …

We associate with every pure flag simplicial complex a standard graded Gorenstein-algebra
whose homological features are largely dictated by the combinatorics and topology of. As …

Numerical semigroups with multiplicity $ m $ are parameterized by integer points in a
polyhedral cone $ C_m $, according to Kunz. For the toric ideal of any such semigroup, the …

We present a procedure that constructs, in a combinatorial manner, a chain complex of free
modules over a polynomial ring in finitely many variables, modulo an ideal generated by …