A central philosophy in commutative algebra is that the (free) resolutions of algebraic objects are the keys to understanding the objects themselves. Indeed, a resolution approximates an algebraic object by simpler algebraic objects and conceals a world of subtle yet essential information. This information is often difficult to extract without realizing additional algebraic structure (i.e. a DG algebra structure) on the resolution itself. In this talk, we introduce the notion of a DG algebra resolution and specialize to the case of edge ideals of split graphs, which are algebraic objects defined by such graphs.
Much of the talk will be devoted to unpacking the terminology in the title, and towards the end, recent results from joint work with Oberlin students will be presented. The talk is intended to be accessible to students who have seen some linear algebra.
Join us on Monday, Nov. 9, for this exciting presentation from Rachel Diethorn, assistant professor of mathematics at Oberlin College & Conservatory. The presentation will begin in Hayes 109 at 3:10 p.m. We hope to see you there!