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Discrete Math

"A spectral gap precludes low-dimensional embeddings"

Assaf Naor, Princeton University

Location:  Hill 705
Date & time: Monday, 17 April 2017 at 2:00PM -



Time: 2:00 PM
Location: Hill 705
Abstract: We prove that if an \(n\)-vertex \(O(1)\)-expander graph embeds with average distortion \(D\) into a finite dimensional normed space \(X\), then necessarily the dimension of \(X\) is at least \(n^{c/D}\) for some universal constant \(c>0\). This is sharp up to the value of the constant \(c\), and it improves over the previously best-known estimate \(mathrm{dim}(X)> c(log n)^2/D^2\).

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