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SUMMARY:Alex Cohen (Yale University)
DTSTART:20200601T180000Z
DTEND:20200601T182500Z
DTSTAMP:20260423T011158Z
UID:CANT2020/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/9/"
 >A Sylvester-Gallai result in the complex plane</a>\nby Alex Cohen (Yale U
 niversity) as part of Combinatorial and additive number theory (CANT 2021)
 \n\n\nAbstract\nWe show that for a Sylvester-Gallai configuration in $\\ma
 thbb{C}^2$ lying on a family \nof $m$ concurrent lines\, each line in the 
 family can contain at most $3m-9$ points of the set\, \nnot including the 
 common point. This implies that many points lying on a family of concurren
 t lines \nmust admit an ordinary line. We also introduce a conjecture whic
 h would improve this bound \nto $m-1$\, which is sharp. Our approach invol
 ves ordering points by their real part\, \nwhich is a new technique for st
 udying complex line arrangements.\n
LOCATION:https://researchseminars.org/talk/CANT2020/9/
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