Pursued work on pseudovarieties of semigroups, mainly using profinite techniques. The main results are the following:

• conditions for the faithful action of a relatively free profinite semigroup on its minimum ideal; this yields several applications in terms of join irreducibility and order primitivity of pseudovarieties of semigroups, including the Krohn-Rhodes pseudovarieties, thereby solving a problem proposed by Rhodes and Steinberg (joint work with O. Klíma);
• a geometric interpretation of the Schützenberger group of a minimal subshift, namely as an inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift (joint with A. Costa);
• a transfer decidability result for pseudovarieties corresponding to varieties of languages of the form Δn in FO[<] quantifier alternation hierarchy (joint with J. Bartoňová, O. Klíma, and M. Kunc); 
• conditions for complete κ-reducibility of pseudovarieties of semigroups of the form DRH (the regular R-classes are groups from a given pseudovariety of groups H), which apply in particular to the case of the pseudovariety DRAb, where Ab is the pseudovariety of all finite Abelian groups (joint work with C. Borlido);
• computation of the closure of rational language in the pro-nilpotent group topology of a free group (joint work with M.H. Shahzamanian and B. Steinberg);
• computation of the rank and of basis of pseudoidentities for pseudovarieties of semigroups defined by several Mal'cev-type nilpotency conditions (joint work with M.H. Shahzamanian);
• reducibility with respect to natural signatures of pointlike and idempotent pointlike problems for the pseudovarieties of all finite semigroups whose subgroups are π-groups, for a fixed set π of primes, and of all finite semigroups whose regular J-classes are products of rectangular bands with groups from a fixed pseudovariety of groups (joint work with J. C. Costa and M. Zeitoun).