We propose a method to unify various stability results about symmetric ideals in polynomial
rings by stratifying related derived categories. We execute this idea for chains of $ GL_n …

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 …

The theory of higher matrix factorizations of a regular sequence f1;:::; fc presented in this
book is an extension of the theory of matrix factorizations of an element in a commutative …

Abstract Let e 1,…, ec be positive integers and let Y⊆ P n be the monomial complete
intersection defined by the vanishing of x 1 e 1,…, xce c. In this paper, we study sharp upper …

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of
minimal free resolutions over the hypersurface. We introduce a new concept of matrix …

Abstract Let (Q, 𝔫, k) be a commutative local Noetherian ring, f 1,…, fca Q-regular sequence
in 𝔫, and R= Q∕(f 1,…, fc). Given a complex of finitely generated free R-modules, we give a …

Research on free resolutions is a core and beautiful area in Commutative Algebra. It
contains a number of challenging conjectures and open problems; many of them are …