UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 12, 2013

939 Evans Hall

3:45PM: Algebra structures on short free resolutions

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.

5:00PM: The Golod Property for Monomial Ideals

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.

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