Parabolic subgroups of Artin groups

Artin groups form an important class of groups that generalize 
braid groups. However, many problems remain open in general for these 
groups. This talk will focus on recent advancements to understand the 
geometry and structure of Artin groups in terms of their parabolic 
subgroups. In particular, we will look at the geometric realization of 
the poset of strict parabolic subgroups, which has recently been shown 
to have systolic geometry in the case of large type Artin groups by 
Cumplido, Martin, and Vaskou. We can then use this geometry to show that 
the set of parabolic subgroups of a large type Artin group is stable 
under arbitrary intersections and forms a lattice under inclusion.