Information theory, graph theory, extremal combinatorics, and coding theory. These include:

1. Shannon theory and information measures with applications to coding, guessing, and statistical inference;
   
   
2. Analytical bounds on graph invariants, graph products, and connections to information theory;
   
   
3. Aspects of Shannon theory in extremal combinatorics and graph theory;
   
   
4. Spectral graph theory;
   
   
5. Concentration-of-measure inequalities from the perspective of information theory, and applications.
   
   
6. Coding theory and error-correcting codes: codes defined on graphs and iterative decoding algorithms, distance spectra and performance bounds of linear codes and code ensembles, bounds on the tradeoff between the performance and encoding/ decoding complexity.