BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Efthymios Sophos (University of Glasgow) DTSTART:20200619T110000Z DTEND:20200619T120000Z DTSTAMP:20260423T021442Z UID:NTdL/8 DESCRIPTION:Title: Sch inzel Hypothesis with probability 1 and rational points\nby Efthymios Sophos (University of Glasgow) as part of Number theory during lockdown\n\ n\nAbstract\nSchinzel's Hypothesis states that there are infinitely many p rimes represented by any integer polynomial satisfying the necessary congr uence assumptions. Equivalently\, there exists at least one prime represen ted by any such polynomial. The problem is completely open\, except in the very special case of polynomials of degree 1. We shall describe our recen t proof of the existence version of Schinzel's Hypothesis for almost all p olynomials\, preprint: https://arxiv.org/abs/2005.02998.\nWe apply our res ult to showing that generalised Châtelet surfaces have a rational point w ith positive probability. These surfaces play an important role in the Bra uer-Manin obstruction in arithmetic geometry\, however\, very little is kn own about their arithmetic.\nThe talk is based on joint work with Alexei S korobogatov.\n LOCATION:https://researchseminars.org/talk/NTdL/8/ END:VEVENT END:VCALENDAR