DMS Algebra Seminar

Time: Nov 15, 2022 (02:30 PM)
Location: Parker Hall 358 and ZOOM



Speaker: Justin Lyle (University of Arkansas)

Title: Stable Theory for Complexes and the Auslander-Reiten Conjecture
Abstract: The Auslander-Reiten conjecture is one of the oldest and most significant conjectures in homological algebra and traces its roots to several natural questions about the representation theory of Artin algebras. In this talk, we will discuss some background for this problem, and some new cases recently established by the speaker. Namely, the Auslander-Reiten conjecture holds for (commutative) local rings with some mild Serre conditions and for (commutative) graded algebras that are reduced. Along the way, we will dip our toes into a version of Auslander-Bridger theory for complexes developed by Yoshino and some extensions of this work that are used in the proofs.