BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julie Bergner (University of Virginia) DTSTART:20210301T133000Z DTEND:20210301T143000Z DTSTAMP:20260422T140031Z UID:BilTop/22 DESCRIPTION:Title: Variants of the Waldhausen S-construction\nby Julie Bergner (Universit y of Virginia) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z 11.\n\nAbstract\nThe S-construction\, first defined in the setting of cofi bration categories by Waldhausen\, gives a way to define the algebraic K-t heory associated to certain kinds of categorical input. It was proved by Galvez-Carrillo\, Kock\, and Tonks that the result of applying this constr uction to an exact category is a decomposition space\, also called a 2-Seg al space\, and Dyckerhoff and Kapranov independently proved the same resul t for the slightly more general input of proto-exact categories. In joint work with Osorno\, Ozornova\, Rovelli\, and Scheimbauer\, we proved that these results can be maximally generalized to the input of augmented stabl e double Segal spaces\, so that the S-construction defines an equivalence of homotopy theories. In this talk\, we'll review the S-construction and the reasoning behind these stages of generalization. Time permitting\, we 'll discuss attempts to characterize those augmented stable double Segal s paces that correspond to cyclic spaces\, which is work in progress with Wa lker Stern.\n LOCATION:https://researchseminars.org/talk/BilTop/22/ END:VEVENT END:VCALENDAR