Information theory, graph theory, extremal combinatorics, and coding theory. This includes:
Shannon theory and information measures with applications to coding, guessing, and statistical inference.
Zero-error information theory and extremal combinatorics.
Graph invariants, graph products, spectral graph theory, and connections to information theory.
Concentration-of-measure inequalities from the perspective of information theory, and applications.
Coding theory: codes on graphs and iterative decoding algorithms, distance spectra and performance bounds of linear codes and code ensembles,
tradeoff between the performance and complexity.