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SUMMARY:Xiumin Du (Northwestern)
DTSTART:20210315T210000Z
DTEND:20210315T220000Z
DTSTAMP:20260423T005652Z
UID:OARS/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/17/">Fa
 lconer's distance set problem</a>\nby Xiumin Du (Northwestern) as part of 
 OARS Online Analysis Research Seminar\n\n\nAbstract\nA classical question 
 in geometric measure theory\, introduced by Falconer in the 80s is\, how l
 arge does the Hausdorff dimension of a compact subset in Euclidean space n
 eed to be to ensure that the Lebesgue measure of its set of pairwise Eucli
 dean distances is positive. In this talk\, I'll report some recent progres
 s on this problem\, which combines several ingredients including Orponen's
  radial projection theorem\, Liu's L^2 identity obtained using a group act
 ion argument\, and the refined decoupling theory. This is based on joint w
 ork with Alex Iosevich\, Yumeng Ou\, Hong Wang\, and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/OARS/17/
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