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SUMMARY:Hong Wang (Institute for Advanced Study\, New Jersey)
DTSTART:20201005T160000Z
DTEND:20201005T165000Z
DTSTAMP:20260423T010011Z
UID:anpdews/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/37/"
 >Distinct distances on the plane</a>\nby Hong Wang (Institute for Advanced
  Study\, New Jersey) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nGiven N 
 distinct points on the plane\, what is the minimal number of distinct dist
 ances between them? This problem was posed by Paul Erdos in 1946 and essen
 tially solved by Guth and Katz in 2010.  \n\nWe are going to consider a co
 ntinuous analogue of this problem\, the Falconer distance problem.  Given 
 a set $E$ of dimension $s>1$\, what can we say about its distance set $\\D
 elta(E)=\\{ |x-y|: x\,y\\in E\\}$? Falconer conjectured in 1985 that $\\De
 lta(E)$ should have positive Lebesgue measure.   In the recent years\,  pe
 ople have attacked this problem in different ways (including geometric mea
 sure theory\, Fourier analysis\, and combinatorics) and made some progress
  for various examples and for some range of $s$.\n
LOCATION:https://researchseminars.org/talk/anpdews/37/
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