BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ryu Tomonaga (U. of Tokyo) DTSTART:20260608T120000Z DTEND:20260608T130000Z DTSTAMP:20260604T204444Z UID:paris-algebra-seminar/231 DESCRIPTION:Title: Non-commutative crepant resolutions of toric singuarities with divisor class group of rank one\nby Ryu Tomonaga (U. of Tokyo) as part of Paris algebra seminar\n\n\nAbstract\nFor a Gorenstein normal sing ularity R\, a non-commutative crepant resolution (NCCR)\, introduced by Va n den Bergh\, is a non-commutative analogue of a crepant resolution and pr ovides a framework for generalizing the derived McKay correspondence. For Gorenstein toric singularities\, it is natural to focus on toric NCCRs\, n amely NCCRs arising from direct sums of divisorial modules. The existence of toric NCCRs has been established in several cases\, including when dimR ≤3\, when Cl(R) is torsion\, when Cl(R)≅Z\, and in some other cases.\n \nIn this talk\, we prove the existence of toric NCCRs for Gorenstein tori c singularities R whose divisor class group Cl(R) has rank one. Moreover\, we classify all toric NCCRs: we show that they are in bijection with the non-trivial upper sets of a certain poset. This classification is new even when Cl(R)≅Z. Using this classification\, we prove that all toric NCCR s of such toric singularities are connected by iterated Iyama--Wemyss muta tions\, and hence are derived equivalent to one another.\n\nIf time permit s\, we will also describe explicitly the quivers with relations of our tor ic NCCRs from the viewpoint of higher-dimensional analogues of dimer model s. More precisely\, although we do not propose a general definition of hig her-dimensional dimer models\, we describe\, in some special cases corresp onding to our toric singularities\, the quivers that would be expected to arise as dual quivers of such objects\, should they exist.\n\nThis talk wi ll take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/231/ END:VEVENT END:VCALENDAR