What is...?

Combinatorial discrepancy asks the following question: Given a ground set U and a collection S of subsets of U, how do we color each element in U red or blue so that each subset in S has almost an equal number of each color? A straightforward idea is to color everyone uniformly and independently at random. Our goal is to improve upon this simple random coloring. In this talk, we will introduce some basics of combinatorial discrepancy, present a simple algorithm, and discuss some applications.