New Mathematical Techniques in Information Theory

Abstract

Information theory is the richer for a surge of recent advances in relevant mathematical techniques. The workshop fostered an exchange of ideas on new mathematical tools which are typically outside the classical toolbox of information theorists and that are yet useful in solving classical and modern problems in information theory and related areas. The focus was on mathematical techniques that are of a general nature and that could benefit a wide class of problems. A number of broad mathematical areas were identified that held promise with established early successes, and key contributors were invited to make presentations and initiate discussions with an emphasis on emergent topics. The areas were: information measures, measure concentration, hypercontractivity and correlation measures, Shannon theory and extremal combinatorics, advanced tools for proving converse results in coding theorems, and recent techniques for proving Gaussian optimality entailing new characterizations of Gaussian distributions.