In recent years, deep results in geometric functional analysis, and specifically in the non-linear theory of Banach spaces, have been successfully applied to solve fundamental problems in several areas of the theory of combinatorial algorithms.
In a somewhat more surprising twist of events, algorithmic insight and tools have been used to revive the non-linear theory of Banach spaces, settling outstanding open questions and generating new research directions. There are many aspects to this fruitful interplay. We will survey a few of them, in the context of algorithmic data analysis.
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