Finite point configurations and the Vapnik-Chervonenkis dimension

Abstract: The Vapnik-Chervonenkis (VC) dimension was invented in 1970 to study learning models. This notion has since become one of the cornerstones of modern data science. This beautiful idea has also found applications in other areas of mathematics. In this talk we are going to describe how the study of the VC-dimension in the context of families of indicator functions of spheres centered at points in sets of a given Hausdorff dimension (or in sets of a given size inside vector spaces over finite fields) gives rise to interesting, and in some sense extremal, point configurations.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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