BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hannah Markwig (Tübingen) DTSTART:20210520T090000Z DTEND:20210520T100000Z DTSTAMP:20260423T024755Z UID:notts_ag/58 DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arithmetic\nby Hannah Markwig (Tübingen) as part of Online Nottingham algebraic g eometry seminar\n\n\nAbstract\nA smooth plane quartic defined over the com plex numbers has precisely 28 bitangents. This result goes back to Pluecke r. In the tropical world\,the situation is different. One can define equiv alence classes of tropical bitangents of which there are 7\, and each has 4 lifts over the complex numbers. Over the reals\, we can have 4\, 8\, 16 or 28 bitangents. The avoidance locus of a real quartic is the set in the dual plane consisting of all lines which do not meet the quartic. Every co nnected component of the avoidance locus has precisely 4 bitangents in its closure. For any field k of characteristic not equal to 2 and with a non- Archimedean valuation which allows us to tropicalize\, we show that a trop ical bitangent class of a quartic either has 0 or 4 lifts over k. This way of grouping into sets of 4 which exists tropically and over the reals is intimately connected: roughly\, tropical bitangent classes can be viewed a s tropicalizations of closures of connected components of the avoidance lo cus. Arithmetic counts offer a bridge connecting real and complex counts\, and we investigate how tropical geometry can be used to study this bridge .\n\nThis talk is based on joint work with Maria Angelica Cueto\, and on j oint work in progress with Sam Payne and Kristin Shaw.\n LOCATION:https://researchseminars.org/talk/notts_ag/58/ END:VEVENT END:VCALENDAR