Information theory, including Shannon theory, information measures, and zero-error information theory.
Combinatorics and graph theory with emphasis on extremal and spectral aspects, graph invariants, graph homomorphisms, and their connections to information theory.
Concentration-of-measure inequalities in information theory and their applications.
Coding theory, including codes on graphs, distance spectra, performance bounds of codes and code ensembles, and performance-complexity tradeoffs.