BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hannah Markwig (U. Tübingen) DTSTART:20201113T150000Z DTEND:20201113T160000Z DTSTAMP:20260423T021054Z UID:LAGARTOS/10 DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arithmetic\nby Hannah Markwig (U. Tübingen) as part of (LAGARTOS) Latin American Real and Tropical Geometry Seminar\n\n\nAbstract\nA smooth plane quartic d efined over the complex numbers has precisely\n28 bitangents. This result goes back to Pluecker. In the tropical world\,\nthe situation is different . One can define equivalence classes of\ntropical bitangents of which ther e are seven\, and each has 4 lifts over\nthe complex numbers. Over the rea ls\, we can have 4\, 8\, 16 or 28\nbitangents. The avoidance locus of a re al quartic is the set in the dual\nplane consisting of all lines which do not meet the quartic. Every\nconnected component of the avoidance locus ha s precisely 4 bitangents in its closure. For any field k of characteristic not equal to 2 and\nwith a non-Archimedean valuation which allows us to t ropicalize\, we\nshow that a tropical bitangent class of a quartic either has 0 or 4\nlifts over k. This way of grouping into sets of 4 which exis ts\ntropically and over the reals is intimately connected: roughly\, tropi cal\nbitangent classes can be viewed as tropicalizations of closures of\n connected components of the avoidance locus. Arithmetic counts offer a\nb ridge connecting real and complex counts\, and we investigate how\ntropic al geometry can be used to study this bridge.\n\nThis talk is based on joi nt work with Maria Angelica Cueto\, and on joint\nwork in progress with Sa m Payne and Kristin Shaw.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/10/ END:VEVENT END:VCALENDAR