BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lisa Seccia (University of Genoa\, Genoa\, Italy) DTSTART:20230113T120000Z DTEND:20230113T130000Z DTSTAMP:20260423T021050Z UID:VCAS/157 DESCRIPTION:Title: W eakly- closed graphs and F-purity of binomial edge ideals\nby Lisa Sec cia (University of Genoa\, Genoa\, Italy) as part of IIT Bombay Virtual Co mmutative Algebra Seminar\n\n\nAbstract\nHerzog et al. characterized close d graphs as the graphs whose binomial edge ideals have a quadratic Groebne r basis. In this talk\, we focus on a generalization of closed graphs\, na mely 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 id eals (associated with a certain polynomial f). In doing so\, we re-prove M atsuda's theorem about the F-purity of binomial edge ideals of weakly-clos ed graphs in prime characteristic and we extend it to generalized binomial edge ideals. \nLastly\, we will discuss some open conjectures on the F-pu rity of binomial edge ideals and on the relation between Knutson ideals an d compatible ideals.\n LOCATION:https://researchseminars.org/talk/VCAS/157/ END:VEVENT END:VCALENDAR