BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, Aus tralia) DTSTART:20211028T110000Z DTEND:20211028T120000Z DTSTAMP:20260423T023051Z UID:LAGOON/51 DESCRIPTION:Title: Finite approximations as a tool for studying triangulated categories\n by Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, Australi a) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOO N)\n\n\nAbstract\nA metric on a category assigns lengths to morphisms\, wi th the triangle inequality holding. This notion goes back to a 1974 articl e by Lawvere. We'll begin with a quick review of some basic constructions\ , like forming the Cauchy completion of a category with respect to a metri c.And then will begin a string of surprising new results. It turns out tha t\, in a triangulated category with a metric\, there is a reasonable notio n of Fourier series\, and an approximable triangulated category can be tho ught of as a category where many objects are the limits of their Fourier e xpansions. And then come two types of theorems: (1) theorems providing exa mples\, meaning showing that some category you might naturally want to loo k at is approximable\, and (2) general structure theorems about approximab le triangulated categories. And what makes it all interesting is (3) appli cations. These turn out to include the proof of a conjecture by Bondal and Van den Bergh\, a major generalization of a theorem of Rouquier's\, and a short\, sweet proof of Serre's GAGA theorem.\n\nhttps://icms-org-uk.zoom. us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09\n\nMeeting ID: 816 0 176 7022\nPasscode: LAGOON\n LOCATION:https://researchseminars.org/talk/LAGOON/51/ END:VEVENT END:VCALENDAR