Combinatorics Seminar: "Combinatorial conditions for virtually Cohen-Macaulay monomial ideals"

Speaker: Jay Yang, Washington University in Saint Louis

Abstract: Virtual resolutions as defined by Berkesch, Erman, and Smith are a way of discussing resolutions over the Cox ring of a toric variety. These resolutions better reflect the geometry associated to a module over a toric variety than the minimal free resolution. This talk will introduce virtual resolutions and discuss examples where the virtual resolution can be computed combinatorically. I will focus on those cases which we call virtually Cohen-Macaulay, corresponding to those modules with short virtual resolutions. In particular, I will discuss an upcoming paper with Adam Van Tuyl as well as a recent paper with Christine Berkesch, Michael C. Loper, and Patricia Klein.

Host: Nathan Lesnevich