Information theory and polyhedral combinatorics

The theory of extended formulations is concerned with the optimal polyhedral representation of a (combinatorial) optimization problem. In this context, information-theoretic methods recently gained significant attention as a convenient way to provide strong lower bounds on the size of such representations. We will provide an introduction to information-theoretic methods in extended formulations, an overview of recent results, and discuss important open problems in extended formulations, which might be amenable to information-theoretic approaches.