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Differential Equations Seminar

Survey on the Falconer distance set problem
Thursday, October 29, 2020
4:00-5:00 PM
Zoom Off Campus Location
Given N distinct points on the plane, what is the minimal number of distinct distances between them? This problem was posed by Paul Erdos in 1946 and essentially solved by Guth and Katz in 2010.

We are going to consider a continuous analog of this problem: the Falconer distance set problem. Given a set $E$ of Hausdorff dimension $s>d/2$ in $\mathbb{R}^d$ , Falconer conjectured that its distance set $\Delta(E)=\{ |x-y|: x, y \in E\}$ should have positive Lebesgue measure. In recent years, people have studied this problem using different techniques in geometric measure theory and Fourier analysis. We are going to study a couple of examples and discuss how people solve the examples using those techniques.

Join Zoom Meeting
https://umich.zoom.us/j/97752443102

Meeting ID: 977 5244 3102
Passcode: 879980

Speaker(s): Hong Wang (IAS)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics