I am a math researcher (M. Zambrano fellow) in the Department of Mathematics at the Universitat Politècnica de Catalunya, a member of the GAPCOMB and GrupsBCN research groups, and an organizer of the Barcelona Weekend in Group Theory.
Previously I have worked at the UPC, the Centre de Recerca Matemàtica (CRM), the Centro de Matemática of the University of Porto, and the University of the Basque Country. I obtained a PhD in mathematics at the Universitat Politècnica de Catalunya under the supervision of Prof. Enric Ventura.
MY LATEST RESEARCH
We consider a natural generalization of the concept of order of an element in a group: an element g in a group G is said to have order k in a subgroup H of G if k is the first strictly positive integer such that g^k belongs to H. We study this notion and its algorithmic properties in the realm of free groups and some related families.
Relative order and spectrum in free and related groups
Intersection configurations in free and free times free-abelian groups
In this paper we delve into the behavior of multiple intersections of subgroups of free and free times free-abelian (FTA) groups with respect to finite generability. We show that a multiple version of Howson property still holds in $\Fn$, and that, in fact, this is the only obstruction for multiple intersection configurations within $\Fn$. Then, we study multiple intersections within FTFA groups...