BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Pauksztello (Lancaster University\, UK) DTSTART:20210617T110000Z DTEND:20210617T120000Z DTSTAMP:20260423T041612Z UID:LAGOON/47 DESCRIPTION:Title: Functorially finite hearts\, simple-minded systems and negative cluster ca tegories\nby David Pauksztello (Lancaster University\, UK) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstra ct\nSimple-minded systems (SMSs) were introduced by Koenig-Liu as an abstr action of nonprojective simple modules in stable module categories: the id ea was to use SMSs as a way to get around the lack of projective generator s to help develop a Morita theory for stable module categories. Recent dev elopments have shown that SMSs in negative Calabi-Yau categories admit mut ation theories and combinatorics that are highly suggestive of cluster-til ting theory. In this talk\, we explain one such development: that negative Calabi-Yau orbit categories of bounded derived categories of acyclic quiv ers serve as categorical models of positive Fuss-Catalan combinatorics and one can think of SMSs as negative cluster-tilting objects. Along the way \, we will make use of the rather surprising observation that in a triangu lated category of finite homological dimension\, functorial finiteness of the heart of a t-structure is related to the property of the heart having enough injectives and enough projectives. This is surprising because it sa ys that some feature of how a heart behaves within an ambient triangulated category can be detected intrinsically in the heart. This talk is based o n joint work with Raquel Coelho Simoes and David Ploog.\n LOCATION:https://researchseminars.org/talk/LAGOON/47/ END:VEVENT END:VCALENDAR