(a) (With S. Margolis and J. Rhodes) Study of the subsemigroup complex of a combinatorial Brandt semigroup; the Dowling geometries and the Rhodes order from the viewpoint of boolean representable simplicial complexes; connections with semigroup theory.

(b) (With F. Soares and M.V. Volkov) Characterization of the locally K-finite varieties of semigroups in terms of forbidden objects, for each Green relation K.

(c) (With M.J.J. Branco and G.M.S. Gomes) Relation between the group rank and the semigroup rank for some classes of groups.

(d) (With N. Szakacs) Inverse semigroups admitting polyhyperbolic Schutzenberger graphs.

(e) (With A. Zakharov) Alternative characterizations of the graded submonoids of free groups; decidability results.