Here is an IN PROGRESS listing of every area I have worked on, roughly in the order of adoption (most ancient first) :
1. Formal Languages and Combinatorics on Words
Results in formal language theory.
1. Contextual languages.
2. Structural equivalence notions for L-systems.
Results in Combinatorics on Words.
1. Self-reading sequences.
2. Recursive function theory, later Computational Complexity
Effective category in recursive function theory.
1. Approximability of the Minimum Entropy Set Cover on sparse instances.
MESC is a problem initially studied by Halperin and Karp (and Cardinal et al.), initially motivated by a problem from computational biology (haplotype resolution)In paper  we give a better approximation guarantee for sparse instances of MESC.
2. The Minimum Entropy Submodular Set Cover problem and its approximability.
In paper  (chronologically the first we wrote on this topic) we generalize the problem to Minimal Entropy Submodular Set Cover (MESSC), a framework that captures many interesting combinatorial subproblems.We give a guarantee for the performance approximation guarantee of the GREEDY algorithm that is almost as good as the one available for (the same algorithm on) MESC