BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julie Desjardins (University of Toronto) DTSTART:20201102T121500Z DTEND:20201102T131500Z DTSTAMP:20260423T023054Z UID:WarsawNT/10 DESCRIPTION:Title: Density of rational points on a family of del Pezzo surface of degree 1< /a>\nby Julie Desjardins (University of Toronto) as part of Warsaw Number Theory Seminar\n\nLecture held in room 403 at IMPAN.\n\nAbstract\nLet k be a number field and X an algebraic variety over k. We want to study the se t of k-rational points X(k). For example\, is X(k) empty? If not\, is it d ense with respect to the Zariski topology? Del Pezzo surfaces are classifi ed by their degrees d (an integer between 1 and 9). Manin and various auth ors proved that for all del Pezzo surfaces of degree >1 it is dense provid ed that the surface has a k-rational point (that lies outside a specific s ubset of the surface for d=2). For d=1\, the del Pezzo surface always has a rational point. However\, we don't know if the set of rational points is Zariski-dense. In this talk\, I present a result that is joint with Rosa Winter in which we prove the density of rational points for a specific fam ily of del Pezzo surfaces of degree 1 over k.\n LOCATION:https://researchseminars.org/talk/WarsawNT/10/ END:VEVENT END:VCALENDAR