Seminar

Commutative Algebra and Algebraic Geometry
Tuesdays, 3:45-6pm in Evans 939
organizer: David Eisenbud
http://hosted.msri.org/alg

3:45 PM
Algebra structures on short free resolutions
Speaker: Lars Christensen

Let $R$ be a quotient of a regular local ring $Q$. If the free resolution of $R$ over $Q$ has length $2$, then its structure is given by the Hilbert--Burch Theorem. For longer resolutions the structure is significantly harder to describe, but for resolutions of length $3$ a partial classification is available. I will discuss some recent progress, achieved in collaboration with Oana Veliche and Jerzy Weyman, towards completion of this classification.

5:00 PM
The Golod Property for Monomial Ideals
Speaker: David Berlekamp

The Golod property for monomial ideals is implied by a simple criterion on GCD's. This can be used to prove that the product of any two monomial ideals is Golod.