I am professor of the Autonomous University of Madrid (UAM) and  member of the Institute of Mathematics (ICMAT).

I co-organize the Pequeño Instituto de Matemáticas (PIM), a weekly problem-solving activity for high school students.

I am editor of Revista Matemática Iberoamericana and Journal of Algebra

Research interests:

  • Group theory: finite and profinite groups, residually finite groups, sofic groups, representation theory, asymptotic invariants of groups.
  • Ring theory: Group rings and crossed products, Noetherian rings, Golod-Shafarevich algebras, Sylvester rank functions
  • Arithmetic geometry: fields of definition and  fields of moduli of algebraic varieties,  Galois groups of number fields.

In the blog