A combination theorem for hierarchically hyperbolic groups

Hierarchically hyperbolic groups (HHGs) and spaces are recently-introduced generalisations of (Gromov-) hyperbolic groups and spaces. Other examples of HHGs include mapping class groups, right-angled Artin groups, and many groups acting properly and cocompactly on CAT(0) cube complexes. In this talk, after introducing and motivating them, I will present a combination theorem for hierarchically hyperbolic groups. As a corollary, any graph product of finitely many HHGs is itself a HHG. Joint work with B. Robbio.