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:20210409T120000Z DTEND:20210409T130000Z DTSTAMP:20260423T035029Z UID:VCAS/77 DESCRIPTION:Title: Hi bi rings and the Ehrhart rings of chain polytopes - Part 1\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 is called a Hibi ring\, in a conference held in Kyoto 1985.\nThis result was published in 1987.\nIt turned out that the Hibi ri ng on a distributive lattice D is the Ehrhart ring of the order polytope o f the poset consisting of join-irreducible elements of D.\nIn the first ta lk\, we recall the definition of Ehrhart rings\, order and chain polytopes \, and Hibi rings.\nWe recall some basic properties of Ehrhart rings and d escribe the canonical module of them.\nUsing these facts\, we state some b asic 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 polytopes of posets.\nIn the second talk\, we focus on the structure of t he canonical modules of the Ehrhart rings of order and chain polytopes of a poset.\nWe describe the generators of the canonical modules in terms of the combinatorial structure of the poset and characterize the level proper ty.\nIf time permits\, we describe the radical of the trace of the canonic al module of these rings and describe the non-Gorenstein locus.\nThis fina l part is a joint-work with Janet Page.\n LOCATION:https://researchseminars.org/talk/VCAS/77/ END:VEVENT END:VCALENDAR