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SUMMARY:Local smoothing and pinned nonempty interior for distance sets
DTSTART:20261023T121500Z
DTEND:20261023T131500Z
DTSTAMP:20261101T232500Z
UID:indico-event-1665@math-events.uni-bonn.de
DESCRIPTION:Speakers: Tainara Borges (Univesity of Bonn)\n\nGiven a compac
 t set $E$ in $R^d$ and a point $y$ in $E$\, define the pinned distance set
  of $E$ at $y$  as$$\\Delta^y(E)=\\{|x-y| \\colon x\\in E\\}.$$Peres and 
 Schlag proved that if the Hausdorff dimension of $E$ is larger than $(d+2)
 /2$\, then there exists a point $y$ in $E$ such that the pinned distance s
 et of $E$ at $y$ has nonempty interior. However\, their threshold is only 
 useful when $d$ is at least $3$ and does not say anything when $d=2$. In t
 his talk\, I will show you how local smoothing estimates for the wave equa
 tion can be used to get a nontrivial threshold for such a problem in the p
 lane and to improve the known threshold in $d=3$. We prove that if $E$ is 
 a compact subset of the plane with Hausdorff dimension at least $7/4$\, th
 en there exists $y$ in $E$ such that the pinned distance set at $y$ contai
 ns an interval. This talk is based on joint work with B. Foster\, Y. Ou\, 
 and E. Palsson. \n\nhttps://math-events.uni-bonn.de/event/1665/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1665/
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