BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Gábor Tardos (Alfréd Rényi Institute)
DTSTART:20200525T130000Z
DTEND:20200525T140000Z
DTSTAMP:20260423T021038Z
UID:EPC/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/7/">Plan
 ar point sets determine many pairwise crossing segments</a>\nby Gábor Tar
 dos (Alfréd Rényi Institute) as part of Extremal and probabilistic combi
 natorics webinar\n\n\nAbstract\nWhat is the largest number $f(n)$ such tha
 t $n$ points in the plane (no three on a line) always determine $f(n)$ pai
 rwise crossing segments. This natural question was asked by Aronov\, Erdo
 ̋s\, Goddard\, Kleitman\, Klugerman\, Pach\, and Schulman in 1991 and the
 y proved $f(n)=\\Omega(\\sqrt{n})$. The prevailing conjecture was that thi
 s bound is far from optimal and $f(n)$ is probably linear in $n$. Neverthe
 less\, this lower bound was not improved till last year\, when  we proved 
 with János Pach and Natan Rubin an almost (but not quite) linear lower bo
 und. Our result gives $f(n)>n/\\exp(O(\\sqrt{\\log n}))$. Determining whet
 her $f(n)$ is truly linear is an intriguing open problem.\n\nPassword: the
  first 6 prime numbers (8 digits in total)\n
LOCATION:https://researchseminars.org/talk/EPC/7/
END:VEVENT
END:VCALENDAR