University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Explicit Euclidean Sections, Codes over the Reals and Expanders

Explicit Euclidean Sections, Codes over the Reals and Expanders

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Discrete Analysis

Here is a basic problem, which comes under various names including “compressed sensing matrices”, Euclidean sections of L1”, “restricted isometries” and more. Find a subspace X or R^N such that every vector x in X has the same L1 and L2 norms (with proper normalization) up to constant factors. It is known that such subspaces of dimension N/2 exist (indeed “most” of them are), and the problem is to describe one explicitly. I will describe some progress towards this problem, based on extending the notion of expander codes from finite fields to the reals.

This talk is part of the Isaac Newton Institute Seminar Series series.

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