BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sebastian Opper (Charles University Prague\, Czech Republic) DTSTART:20210304T120000Z DTEND:20210304T130000Z DTSTAMP:20260423T024800Z UID:LAGOON/36 DESCRIPTION:Title: Spherical objects on cycles of projective lines and transitivity\nby S ebastian Opper (Charles University Prague\, Czech Republic) as part of Lon gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\ nPolishchuk showed that spherical objects in the derived category of any c ycle of projective lines yield solutions of the associative Yang-Baxter eq uation which raises the question whether one can classify spherical object s. He further posed the question whether the group of derived auto-equiva lences of a cycle acts transitively on isomorphism classes of spherical ob jects. Partial solutions to both problems were given in works of Burban-Kr eussler and Lekili-Polishchuk. A theorem of Burban-Drozd establishes a co nnection between the derived category of any cycle of projective lines wit h the derived category of a certain gentle algebra which can be modeled by a (toplogical) surface and which allows us to translate algebraic informa tion in the derived category such as objects into geometric information on the surface such as curves. I will explain how the result of Burban-Drozd can be used to find a similar model for the derived category of a cycle. Afterwards we discuss how this can be exploited to classify spherical obje cts and establish transitivity. Further applications include a description of the group of derived auto-equivalences of a cycle and faithfulness of a certain group action as defined by Sibilla.\n LOCATION:https://researchseminars.org/talk/LAGOON/36/ END:VEVENT END:VCALENDAR