(a) Boolean representable simplicial complexes of dimension 2: homotopy type, characterization of the sequentially Cohen-Macaulay complexes, EL-labellings, characterization of the lattices of flats (with Stuart Margolis and John Rhodes).
(b) Delay pseudovarieties, semaphore codes and random walks: study of random walks on the Cayley graphs of right congruences on De Bruijn's semigroups, profinite limits (with John Rhodes and Anne Schilling).
(c) Takahasi semigroups: characterization of semigroups where each ascending chain of bounded rank subsemigroups is stationary (with M\'ario Branco and Gracinda Gomes).
(d) Locally finite varieties of semigroups relatively to some Green's relation: study of varieties of (inverse, completely regular) semigroups where each finitely generated subgroups has only finitely many K-classes for K = J,D,R,L,H (with Filipa Soares).
(e) Uniformly continuous automorphisms of self-similar groups for the tree metric: all automorphisms of the lamplighter group are uniformly continuous for the metric defined through the first level where two elements of the group (seen as tree automorphisms) differ (with Francesco Matucci).
(f) Hereditarily continuous functions: for a pseudovariety V of monoids of certain type (p-groups, groups, aperiodic monoids, monoids), characterization of the functions from A* (or N^k or Z^k) into Z which are uniformly continuous with respect to the pro-W metric for every pseudovariety W of V (with Jean-Eric Pin).