My research interests lie in group theory and its interplay with geometry and model theory.

 

More precisely, I am interested in the study of right-angled Artin groups (RAAGs) and their generalisations from different perspectives:

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• algebraic and combinatorial - RAAGs are defined by presentations associated with labelled graphs. From this perspective, they are part of the larger class of Artin groups. In this line, I am interested in the relation between the algebraic properties of the group and the combinatorial properties of the defining graphs. Specifically, the solution to the isomorphism problem, the embedabbility problem and the classification up to commensurability in graph theoretic terms.

• geometric - RAAGs are one of the main examples of cubulated groups and hierarchically hyperbolic groups. In this line, I am interested in their coarse geometry, namely the structure of their asymptotic cones and the classification up to quasi-isometry.

• algorithmic and cohomological - RAAGs are the main source of groups that have subgroups with interesting algorithmic and cohomological properties. In this area, I am interested in the connection between the finiteness properties of the subgroup and the decidability of the algorithmic problems. 

• model-theoretic - In this line I am interested in the study of the universal and elementary theory of a RAAG as well as the stability of their theory.