AAG Seminar: Constructing Virtual Resolutions

Speaker: Jay Yang, Washington University in St. Louis

Abstract: Virtual resolutions aim to be a syzygetic tool to study modules over certain multigraded rings, specifically the Cox rings of toric varieties. Little is known in general about how to construct short virtual resolutions for arbitrary graded modules. I will discuss both recent work with Adam Van Tuyl as well as previous work with Berkesch, Klien, and Loper on constructing virtual resolutions for monomial ideals. I will also discuss more a more recent breakthrough on the construction of virtual resolutions for toric ideals inspired by results related to mirror symmetry.