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UID:6543@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210211T140000
DTEND;TZID=Europe/Paris:20210211T150000
DTSTAMP:20250118T133219Z
URL:https://www.i2m.univ-amu.fr/evenements/measuring-the-local-non-convexi
 ty-of-real-algebraic-plane-curves/
SUMMARY:Miruna-Stefana Sorea (Scuola Internazionale Superiore di Studi Avan
 zati (SISSA)\, Trieste\, Italy): Measuring the local non-convexity of real
  algebraic plane curves
DESCRIPTION:Miruna-Stefana Sorea: \n\n\n\n\n\n\n\n\n\nWe study the real Mil
 nor fibre of real bivariate polynomial functions vanishing at the origin\,
  with an isolated local minimum at this point. We work in a neighbourhood 
 of the origin in which its non-zero level sets are smooth Jordan curves. W
 henever the origin is a Morse critical point\, the sufficiently small leve
 ls become boundaries of convex disks. Otherwise\, they may fail to be conv
 ex\, as was shown by Coste.\nIn order to measure the non-convexity of the 
 level curves\, we introduce a new combinatorial object\, called the Poinca
 ré-Reeb tree\, and show that locally the shape stabilises and that no spi
 ralling phenomena occur near the origin. Our main objective is to characte
 rise all topological types of asymptotic Poincaré-Reeb trees. To this end
 \, we construct a family of polynomials with non-Morse strict local minimu
 m at the origin\, realising a large class of such trees.\nAs a preliminary
  step\, we reduce the problem to the univariate case\, via the interplay b
 etween the polar curve and its discriminant. Here we give a new and constr
 uctive proof of the existence of Morse polynomials whose associated permut
 ation (the so-called “Arnold snake”) is separable\, using tools inspir
 ed from Ghys’s work.\n\n\n\n\n\n\n\n\n\n\n\nhttps://arxiv.org/abs/1907.0
 8585\n\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Miruna-Stefana_Sorea.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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