BarCeloNa Group Theory

GrupsBCN is a research group in group theory based in Barcelona


Welcome to the web page of the Barcelona Research Group in Geometric, Algorithmic and Combinatorial Group Theory. We are a catalan research team working at the Barcelona area (most of us carry our teaching and research activities in one of the Mathematics Departments of the Universitat Politècnica de Catalunya or of the Universitat Autònoma de Barcelona).

Our mathematical research interests include (but are not limited to) the following three aspects:

  • geometric methods in Group Theory: Cayley graphs, hyperbolicity, quasi-isometries, asymptotic invariants, lattice of subgroups of a free group, Stallings graphs, train-tracks for automorphisms of free groups, and group actions on low-dimensional spaces.
  • combinatorial methods in Group Theory: fixed points, retracts, inertia, algebraic extensions, closures and intersections of subgroups, residual finiteness, conjugacy separability, hopfianity, equations over groups, limit groups, isoperimetric functions, growth, automata groups, subgroup distortion,  Thomson's group, and amenability.
  • algorithmic aspects of Group Theory: solvability and unsolvability, word and conjugacy problems, twisted conjugacy problem and orbit decidability, asymptotic behavior of algorithmic problems, worst-case and generaic-case complexity, and applications to group-based cryptography.

One of our main regular activities is the Barcelona Group Theory Seminar (see the seminar web page to see the exact current details and the historic activity), hosted once a week at the Centre de Recerca Matemàtica; and the Barcelona Weekend in Group Theory, a series of conferences of small format hosted in Barcelona once a year.

We maintain close scientific contacts and collaborations with many other research teams in Group Theory at different universities around the world. We also regularly host visiting researchers, postdocs and students from abroad which come to Barcelona to work and collaborate with us.

Along the years, our research group has been (and is currently) supported through several research projects funded by different organizations, mainly the Catalan and Spanish governments.