In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions
are k-step linear; surprisingly, the bounds are logarithmic in the number of variables. We …

Estimates are obtained for the degrees of minimal syzygies of quotient algebras of
polynomial rings. For a class that includes Koszul algebras in almost all characteristics …

A Koszul algebra R is a N-graded K-algebra whose residue field K has a linear free
resolution as an R-module. We present various characterizations of Koszul algebras and …

This paper is an expanded version of three talks given by I. Peeva during the Introductory
Workshop in Commutative Algebra at MSRI in August 2013. It is a survey on infinite graded …

On the subadditivity problem for maximal shifts in free resolutions Page 256 Commutative
Algebra and Noncommutative Algebraic Geometry, II MSRI Publications Volume 68, 2015 …

Let R= S/I be a graded algebra with ti and T i being the minimal and maximal shifts in the
minimal graded free resolution of R at degree i. We prove that tn≤ t 1+ T n− 1 for all n. As a …

Let $ I $ be a monomial ideal in the polynomial ring $ S $ generated by elements of degree
at most $ d $. In this paper, it is shown that, if the $ i $-th syzygy of $ I $ has no element of …

The purpose of this paper is to give a simple geometric construction of ideals whose
Castelnuovo-Mumford regularity is large compared to the generating degree. Moreover, our …

We investigate decompositions of Betti diagrams over a polynomial ring within the
framework of Boij-Söderberg theory. That is, given a Betti diagram, we decompose it into …

This paper concerns the study of a class of clutters called simplicial subclutters. Given a
clutter C and its simplicial subclutter D, we compare some algebraic properties and …