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SUMMARY:The magic triangle & other stories
DTSTART:20250617T075000Z
DTEND:20250617T085000Z
DTSTAMP:20260610T152700Z
UID:indico-event-14361@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ludovic Morin (Université de Bordeaux)\n\nLet P_K(n
 \,m) be the probability that the convex hull of n+m points drawn uniformly
  and independently in a convex domain K of area 1 (in the plane) has exact
 ly n vertices.It all started with the study of the probability P_K(4\,0)\,
  that goes back to the end of the 19th century and Sylvester’s four poin
 ts problem\, which was solved by Blaschke in 1917. Since then\, more gener
 al results have followed for P_K(n\,0) when K is a parallelogram\, a trian
 gle or a circle\, as well as other asymptotic results.In particular\, a su
 rprising result by Bárány et al. in 2000 gives the exact probability tha
 t n i.i.d. uniform points in a triangle form a convex chain between two ch
 osen vertices (i.e. the boundary of the convex hull of the n points togeth
 er with two vertices of the triangle contains the n points).In the first p
 art of this presentation\, after introducing this tool and its properties\
 , I’ll try to demonstrate how a substantial number of the results that h
 ave emerged around P_K(n\,q) can be seen as a direct or indirect consequen
 ce of this so-called “magic” triangle. In the second part of the talk\
 , I will study a generalized version of this magic triangle\, that allowed
  us to reach some recent results for P_K(n\,m).\n\nhttps://indico.math.cnr
 s.fr/event/14361/
LOCATION:Salle F. Pellos (1R2-207)
URL:https://indico.math.cnrs.fr/event/14361/
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