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TZID:Europe/Vienna
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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20200807T115021Z
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\, IST Austria
ORGANIZER:hwagner@ist.ac.at
SUMMARY:Special GeomTop seminar: "\;Sylvester's Four-Point Problem on O
rder Types"\;
URL:https://talks-calendar.app.ist.ac.at/events/2712
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