Combinatorial semigroup theory: generating sets for semigroups and defining semigroups by presentations (generators and defining relations); presentations for substructures and algebraic constructions;

Subsemigroups: index and rank; 

Group and semigroup presentations;

Transformation semigroups: properties of finite and infinite semigroups of mappings from a set into itself;

 Machine and languages (theoretical computer science) in algebra: automatic structures, decidability;

Combinatorics of permutations, words, etc: pattern classes, decidability questions in combinatorics; 

Computational algebra: algorithms and packages for computing with algebraic structures.