Abstract: We are going to explore a variety of emerging connections between combinatorics, geometry, data science. These investigations are going to center around two beautiful classical concepts. The first is the Vapnik-Chervonenkis dimension, invented circa 1970 as one of the key tools in learning theory. The second is the energy integral and its discrete counterparts, used to study (Hausdorff) dimensionality of sets in Euclidean space. The flow of ideas is in both directions. The participants will have the opportunity to explore applications of learning theory ideas in geometric combinatorics and geometric measure theory. On the other hand, they will also be able to apply concepts from combinatorics and geometry to the study of the "effective dimensionality" of large data sets and the associated optimization problems. Both computational and theoretical aspects of these problems will be explored. The participants are expected to have a background in basic real analysis, probability, and (intermediate) python programming.