DMS Algebra Seminar

Time: Aug 23, 2022 (02:30 PM)
Location: 358 Parker Hall

Speaker: Michael Brown (Auburn)
Title: Short virtual resolutions in Picard rank 2
Abstract: Let \(X\) be a toric variety with coordinate ring \(S\). A virtual resolution of a graded \(S\)-module \(M\) is a generalization of the notion of a free resolution; more precisely, it is a complex that is a free resolution of \(M\) up to so-called irrelevant homology. Berkesch-Erman-Smith conjectured a version of Hilbert's Syzygy Theorem for virtual resolutions; one of the goals of this project is to prove this conjecture in Picard rank 2. In this talk, I'll mostly give background on virtual resolutions and Berkesch-Erman-Smith's conjecture.  This is joint work with Mahrud Sayrafi (Minnesota).