BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Álvaro Sánchez (Universidad de Murcia\, Spain) DTSTART:20260128T130000Z DTEND:20260128T140000Z DTSTAMP:20260423T023052Z UID:LAGOON/108 DESCRIPTION:Title: Abstract representation theory of quivers and spectral Picard groups\ nby Álvaro Sánchez (Universidad de Murcia\, Spain) as part of Longitudin al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nWhile the (derived) representation theory of quivers over a field is by now well -understood\, much less is known when moving to coefficients in the intege rs or an arbitrary commutative ring. In this talk\, we take a rather radic al but well-founded approach: it has recently been observed that certain w ell-known symmetries of categories of representations (tilting results) ar e actually mere consequences of the stability of the coefficients involved \, and so they exist in a much broader generality\, often for the correspo nding representations in any stable homotopy theory — this includes arbi trary rings\, schemes\, dg algebras\, or ring spectra. For a finite acycli c quiver Q\, we present here a method for producing universal autoequivale nces of representations C^Q in any stable ∞-category C\, which are the e lements of the spectral Picard group of Q. This is based on an abstract eq uivalence of C^Q with a certain mesh ∞-category of representations of th e Auslander–Reiten quiver Γ_Q. Then our universal equivalences arise fr om symmetries of Γ_Q\, and thus yield abstract versions of key functors i n classical representation theory — e.g. the Auslander-Reiten translatio n\, the Serre functor\, etc. Moreover\, for representations of trees this allows us to realize the whole derived Picard group over a field as a fact or of the spectral Picard group.\n LOCATION:https://researchseminars.org/talk/LAGOON/108/ END:VEVENT END:VCALENDAR