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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20260404T110309Z
UID:5e42869846e76145036229@ist.ac.at
DTSTART:20200305T130000
DTEND:20200305T141500
DESCRIPTION:Speaker: Emo Welzl\nhosted by Uli Wagner\nAbstract: Roughly spe
 aking\, a planar order type is a point set where we forget aboutthe coordi
 nates of the points\, but keep for each pair of points theinformation whic
 h of the other points lie left and right of the lineconnecting these two p
 oints. For example\, assuming no three points lie on acommon line\, there 
 are exactly two 4-point order types: four pointswhich are vertices of a co
 nvex quadrilateral\, or three points with thefourth point inside the trian
 gle formed by these three points.We consider such order types of points in
  general position in the planeand show that the expected number of extreme
  points in such an n-pointorder type\, chosen uniformly at random from all
  such order types\, is4+o(1). This implies that order types read off unifo
 rm random samples of aconvex planar domain\, smooth or polygonal\, are con
 centrated\, i.e. wetypically encounter only a vanishing fraction of all or
 der types via such asampling.As a crucial step we analyze the orientation 
 preserving symmetries oforder types of finite point sets in the projective
  plane\, along the linesof Felix Klein's characterization of the finite su
 bgroups of the isometriesof the 2-dimensional sphere.Joint work with Xavie
 r Goaoc.
LOCATION:Mondi Seminar Room 3\, Central Building\, ISTA
ORGANIZER:hwagner@ist.ac.at
SUMMARY:Emo Welzl: Special GeomTop seminar: &quot\;Sylvester's Four-Point P
 roblem on Order Types&quot\;
URL:https://talks-calendar.ista.ac.at/events/2712
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