Information Inequalities and Spectral Theory of Graphs.

Universal inequalities satisfied by entropies of any collection of random variables and their joints is of fundamental importance both in Information Theory and applications, such as e.g. algorithmic complexity, cryptography, causal inference or complex systems. In this talk I will explain the set of techniques relating information inequalities and other information theoretic questions to spectral properties of graphs, hypergraphs and simplicial complexes.