BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julie Desjardins (University of Toronto Mississauga) DTSTART:20201005T130000Z DTEND:20201005T133000Z DTSTAMP:20260423T021238Z UID:POINT/13 DESCRIPTION:Title: D ensity of rational points on a family of del Pezzo surface of degree 1 \nby Julie Desjardins (University of Toronto Mississauga) as part of POINT : New Developments in Number Theory\n\n\nAbstract\nLet $k$ be a number fie ld and $X$ an algebraic variety over $k$. We want to study the set of $k$- rational points $X(k)$. For example\, is $X(k)$ empty? If not\, is it dens e with respect to the Zariski topology? Del Pezzo surfaces are classified by their degrees $d$ (an integer between 1 and 9). Manin and various autho rs proved that for all del Pezzo surfaces of degree $d>1$\, $X(k)$ is dens e provided that the surface has a $k$-rational point (that lies outside a specific subset of the surface for $d=2$). For $d=1$\, the del Pezzo surfa ce always has a rational point. However\, we don't know if the set of rati onal points is Zariski-dense. In this talk\, I present a result that is jo int with Rosa Winter in which we prove the density of rational points for a specific family of del Pezzo surfaces of degree 1 over $k$.\n LOCATION:https://researchseminars.org/talk/POINT/13/ END:VEVENT END:VCALENDAR