We are interested in various topics in Algebra and its applications. Our research topic include Geometric and combinatorial group theory: discrete and pro-p groups, homological and homotopical properties of groups, growth and dynaics in groups, finiteness properties, among others. We also study algebras with polynomial identities: bases of identities, gradings and involutions on algebras and the corresponding identities, actions and invariant theory of classical groups. We conduct research on Lie algebras and quantum groups, representations and algebraic groups. Another line of research includes Algebraic geometry and its applicatios to Coding theory: curves with many rational points, finite geometries, Goppa codes, Numerical semigroups, Prym varieties and Weierstrass point theory.