BEGIN:VCALENDAR
CALSCALE:GREGORIAN
PRODID:iCalendar-Ruby
VERSION:2.0
BEGIN:VEVENT
DESCRIPTION: A pseudocircle is a simple closed curve in the plane. An inter
secting arrangement of pseudocircles is a finite collection of pseudocircle
s so that any two intersect in exactly two points where they cross. Grünbau
m conjectured in the 1970's that in the case of simple arrangements there a
re at most 2n - 2 digon cells\, i.e. cells which have exactly two crossings
on its boundary. I will present a result by Agarwal et al. (2004) which pr
oves this conjecture for the special case of cylindrical arrangements. Base
d on that we show that the conjecture also holds whenever the arrangement c
ontains three pseudocircles which pairwise form a digon cell. Moreover\, I
will present a result concerning the number of triangles in digon free arra
ngements\, which disproves another conjecture by Grünbaum. (joint with S.Fe
lsner and M.Scheucher)
DTSTAMP:20220511T193800
DTSTART:20220516T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)\n
SEQUENCE:0
SUMMARY:Sandro Roch (Technische Universität Berlin): Arrangements of Pseudo
circles: On Digons and Triangles
UID:107920318@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220516-C-Roch.html
END:VEVENT
END:VCALENDAR