__Project
title:__
Connections between combinatorics, geometry, and data science: theory and
computation

__
Advisors:__ Alex
Iosevich (University of Rochester), Steven J. Miller (Williams College: In
Residence), Eyvi Palsson (Virginia Tech)

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.

Note: Right now people's schedules are in flux, so it is unclear who will be in residence in addition to Professor Miller, and for what dates.

Readings and additional items will be added later. This page is under construction.