BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raymond van Bommel (University of Bristol) DTSTART:20260610T040000Z DTEND:20260610T050000Z DTSTAMP:20260604T163127Z UID:UNSW-NTSeminar/29 DESCRIPTION:Title: Reduction of plane quartics and Cayley octads\nby Raymond van Bommel (University of Bristol) as part of UNSW Number Theory Seminar\n\nLe cture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nFor a long tim e\, number theorists have been interested in studying the reduction modulo $p$ of algebraic varieties defined over number fields. For example\, in t he case of an elliptic curve $E$\, where we distinguish between good\, mul tiplicative\, and additive reduction\, the Birch and Swinnerton-Dyer conje cture predicts that the reduction plays a crucial role in understanding th e rank of $E(\\mathbb{Q})$. For hyperelliptic curves $y^2 = f(x)$\, the re duction has been studied extensively through the Weierstrass points\, i.e. the roots of $f(x)$. In this talk\, I will tell about recent work joint w ith Jordan Docking\, Vladimir Dokchitser\, Reynald Lercier\, Elisa Lorenzo Garcia\, and Andreas Pieper\, in which we study the situation for the fir st case of non-hyperelliptic curves: plane quartics. As a result of numero us computations\, we made a prediction how the reduction type of a plane q uartic can be determined from the Cayley octad\, a set of eight points in $\\mathbb{P}^3$ associated to the curve.\n LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/29/ END:VEVENT END:VCALENDAR