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Embedding Structures with Distortion

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There is a wide variety of structures that are equipped with a distance. A familiar example is three-dimensional Euclidean space: here the distance is the length of the straight line segment joining two points. In this example there is an additional feature: the presence of vector addition and scalar multiplication. There are examples, however, that do not possess such additional features, and it is an important question to determine whether such arbitrary structures can be embedded into ones with a vector structure like Euclidean space. This has consequences for large data, algorithms, compressed sensing, etc., some of which have emerged in unexpected and surprising ways.

This talk is part of the Trinity Mathematical Society series.

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