BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrés Jaramillo-Puentes (U. Duisburg-Essen) DTSTART:20220603T140000Z DTEND:20220603T150000Z DTSTAMP:20260423T021056Z UID:LAGARTOS/44 DESCRIPTION:Title: Enriched tropical intersection\nby Andrés Jaramillo-Puentes (U. Dui sburg-Essen) as part of (LAGARTOS) Latin American Real and Tropical Geomet ry Seminar\n\n\nAbstract\nTropical geometry has been proven to be a powerf ul computational tool in enumerative geometry over the complex and real nu mbers. In this talk we present an example of a quadratic refinement of thi s tool\, namely a proof of the quadratically refined Bézout’s theorem f or tropical curves. We recall the necessary notions of enumerative geometr y over arbitrary fields valued in the Grothendieck-Witt ring. We will ment ion the Viro’s patchworking method that served as inspiration to our con struction based on the duality of the tropical curves and the refined Newt on polytope associated to its defining polynomial. We will prove that the quadratically refined multiplicity of an intersection point of two tropica l curves can be computed combinatorially. We will use this new approach to prove an enriched version of the Bézout theorem and of the Bernstein–K ushnirenko theorem\, both for enriched tropical curves. Based on a joint w ork with S. Pauli.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/44/ END:VEVENT END:VCALENDAR