BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Navid Nabijou (Cambridge) DTSTART:20200924T140000Z DTEND:20200924T150000Z DTSTAMP:20260423T005758Z UID:notts_ag/27 DESCRIPTION:Title: Degenerating tangent curves\nby Navid Nabijou (Cambridge) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt is well-kn own that a smooth plane cubic $E$ supports $9$ flex lines. In higher degre es we may ask an analogous question: "How many degree $d$ curves intersect $E$ in a single point?" The problem of calculating such numbers has fasci nated enumerative geometers for decades. Despite being an extremely classi cal and concrete problem\, it was not until the advent of Gromov-Witten in variants in the 1990s that a general method was discovered. The resulting theory is incredibly rich\, and the curve counts satisfy a suite of remark able properties\, some proven and some still conjectural. In this talk I w ill discuss joint work with Lawrence Barrott\, in which we study the behav iour of these tangent curves as the cubic $E$ degenerates to a cycle of li nes. Using the machinery of logarithmic Gromov-Witten theory\, we obtain d etailed information concerning how the tangent curves degenerate along wit h $E$. The theorems we obtain are purely classical\, with no reference to Gromov-Witten theory\, but they do not appear to admit a classical proof. No prior knowledge of Gromov-Witten theory will be assumed.\n LOCATION:https://researchseminars.org/talk/notts_ag/27/ END:VEVENT END:VCALENDAR