Back to Commutative Algebra Seminar: Spring 2024
Commutative Algebra Seminar
Date: Friday, Apr 12, 2024
Time: 2:00PM - 3:00PM
Location: LCB 215
Tim Tribone
University of Utah
Title |
Matrix factorizations and Knorrer’s Theorem |
Abstract |
A local ring is said to have finite Cohen-Macaulay type if there are only finitely many indecomposable maximal Cohen-Macaulay modules up to isomorphism. The classification of such rings is far from complete; we understand small dimensions and the case of a hypersurface ring, but that is essentially it. This talk will focus on the key tool used in proving the hypersurface case (matrix factorizations). We will introduce the basics of the theory of matrix factorizations and explain how they are used in the classification of hypersurface rings of finite Cohen-Macaulay type. Along the way, we will address some natural questions inspired by the classification regarding “d-fold” matrix factorizations. This is joint work with Graham Leuschke. |
Commutative Algebra