Analysis Seminar

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Falconer's distance set problem and weighted restriction estimates

Speaker: Yumeng OU, CUNY Baruch College

Location: Warren Weaver Hall 1302

Date: Thursday, November 29, 2018, 11 a.m.

Synopsis:

Any compact set $E$ in $\mathbb{R}^d$ determines a distance set
$\Delta(E)$ consisting of all distinct distances generated by points in
$E$. It is a famous conjecture of Falconer that if $E$ has Hausdorff
dimension larger than $d/2$, then $\Delta{E}$ has positive Lebesgue
measure. This conjecture is still open in all dimensions. In this talk,
I'll present some recent progress towards the conjecture, via new tools
from Fourier restriction estimates and geometric measure theory. This is
based on joint works with Xiumin Du, Larry Guth, Alex Iosevich, Hong Wang,
Bobby Wilson, and Ruixiang Zhang.