# Lisa Seccia: Weakly-closed graphs and F-purity of binomial edge ideals

**Time: **
Mon 2022-10-24 15.15 - 16.15

**Location: **
Zoom

**Video link: **
Meeting ID: 661 4318 1157

**Participating: **
Lisa Seccia (Genoa)

### Abstract

In a work by Herzog et al., the authors characterize closed graphs as the graphs whose binomial edge ideals have quadratic Groebner bases (with respect to a diagonal term order). In this talk, we focus on a generalization of closed graphs, namely weakly-closed graphs (or co-comparability graphs). Building on known results about Knutson ideals of generic matrices, we characterize weakly-closed graphs as the only graphs whose binomial edge ideals are Knutson ideals (associated with a certain polynomial f). In doing so, we re-prove Matsuda's theorem about the F-purity of binomial edge ideals of weakly-closed graphs in positive characteristic and we extend it to generalized binomial edge ideals. Lastly, we will discuss some open conjectures on the F-purity of binomial edge ideals.