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UID:d839896567cec1d074f017a893930209
CATEGORIES:Discrete Math
CREATED:20221116T131733
SUMMARY:Convex polytopes from fewer points  
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: Finding the smallest integer N=ES_d(n) such that in every configu
 ration of N points in R^d in general position there exist n points in conve
 x position is one of the most classical problems in extremal combinatorics,
  known as the Erd?s-Szekeres problem. In 1935, Erd?s and Szekeres famously 
 conjectured that ES_2(n)=2^{n?2}+1 holds, which was nearly settled by Suk i
 n 2016, who showed that ES_2(n)?2^{n+o(n)}. We discuss a recent proof that 
 ES_d(n)=2^{o(n)} holds for all d?3. Joint work with Dmitrii Zakharov.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract</strong>: Finding the smallest integer N=ES_d(n) such t
 hat in every configuration of N points in R^d in general position there exi
 st n points in convex position is one of the most classical problems in ext
 remal combinatorics, known as the Erd?s-Szekeres problem. In 1935, Erd?s an
 d Szekeres famously conjectured that ES_2(n)=2^{n?2}+1 holds, which was nea
 rly settled by Suk in 2016, who showed that ES_2(n)?2^{n+o(n)}. We discuss 
 a recent proof that ES_d(n)=2^{o(n)} holds for all d?3. Joint work with Dmi
 trii Zakharov.</p>
CONTACT:Cosmin Pohoata (IAS)
DTSTAMP:20260828T104010
DTSTART;TZID=America/New_York:20221121T140000
DTEND;TZID=America/New_York:20221121T150000
SEQUENCE:0
TRANSP:OPAQUE
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