Mathematics Colloquia and Seminars

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Description

Random linear embeddings, which embed points in a high-dimensional space into a low-dimensional space while preserving distances up to a multiplicative factor, are central in many areas of pure and applied mathematics. Unfortunately, many random linear maps of interest fail to be embeddings. But they fail in an interesting way, never squashing distinct points to be close but sometimes stretching distances out by a large factor. That is, these maps are still injective (in a robust, quantitative way). This talk will describe a new theory of random injections, showing these maps are still useful in applications and describing mathematical tools for establishing the injectivity property. Examples of this theory will be provided for tensor-structured linear maps. No prior knowledge of random matrix theory or dimensionality reduction will be assumed.