BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mitsuhiro Miyazaki (Kyoto University of Education) DTSTART:20210416T120000Z DTEND:20210416T130000Z DTSTAMP:20260423T020957Z UID:VCAS/78 DESCRIPTION:Title: Hi bi rings and the Ehrhart rings of chain polytopes - Part 2\nby Mitsuhi ro Miyazaki (Kyoto University of Education) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\nIn 1985\, Stanley submitted a p aper titled "Two Poset Polytopes"\, which was published in 1986\, in which he defined the order and chain polytopes of a finite partially ordered se t (poset for short).\nOn the other hand\, Hibi presented a notion of an al gebra with straightening law (ASL for short) on a finite distributive latt ice\, which nowadays called a Hibi ring\, in a conference held in Kyoto 19 85.\nThis result was published in 1987.\nIt turned out that the Hibi ring on a distributive lattice D is the Ehrhart ring of the order polytope of t he poset consisting of join-irreducible elements of D.\nIn the first talk\ , we recall the definition of Ehrhart rings\, order and chain polytopes\, and Hibi rings.\nWe recall some basic properties of Ehrhart rings and desc ribe the canonical module of them.\nUsing these facts\, we state some basi c facts of Hibi rings\, i.e.\, the Ehrhart rings of the order polytopes of posets.\nWe also state some basic facts of the Ehrhart rings of chain pol ytopes of posets.\nIn the second talk\, we focus on the structure of the canonical modules of the Ehrhart rings of order and chain polytopes of a p oset.\nWe describe the generators of the canonical modules in terms of the combinatorial structure of the poset and characterize the level property. \nIf time permits\, we describe the radical of the trace of the canonical module of these rings and describe the non-Gorenstein locus.\nThis final p art is a joint-work with Janet Page.\n LOCATION:https://researchseminars.org/talk/VCAS/78/ END:VEVENT END:VCALENDAR