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
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Compressed subroups of free groups are inert
This post discusses the proof that every compressed subgroup of a finitely generated free group is inert, solving a conjecture of Dicks and Ventura.