BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miruna-Ştefana Sorea (SISSA) DTSTART:20230112T151500Z DTEND:20230112T170000Z DTSTAMP:20260422T065510Z UID:CJCS/96 DESCRIPTION:Title: Po incaré-Reeb Graphs of Real Algebraic Domains\nby Miruna-Ştefana Sore a (SISSA) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr act\nConsider a real bivariate polynomial function that has a strict local minimum at the origin and that vanishes at this point. In a sufficiently small neighborhood of the origin\, the non-zero level curves of this funct ion are smooth Jordan curves. Whenever the origin is a Morse strict local minimum\, the small enough level curves become boundaries of convex topolo gical disks. Otherwise\, the levels may be non-convex\, as was proven by M . Coste. In order to measure this non-convexity\, we introduce a combinato rial object called the Poincaré-Reeb tree associated to a level curve and to a projection direction. Our goal is to characterize all topological ty pes of Poincaré-Reeb trees. I will explain how to construct a family of p olynomials that realizes a large class of these trees. Moreover\, in a joi nt work with Arnaud Bodin and Patrick Popescu-Pampu\, we extend the previo us method of study of non-convexity to real algebraic domains.\n LOCATION:https://researchseminars.org/talk/CJCS/96/ END:VEVENT END:VCALENDAR