Parabolic subgroups of two-dimensional Artin groups (en distanciel)

Parabolic subgroups are central in the theory of Artin groups. It is not known whether the intersection of parabolic subgroups of any Artin group is a parabolic subgroup. It is believed that it is always the case, but the answer is only known for some families of Artin groups. A recent article by Cumplido, Martin and Vaskou introduces a geometric strategy for approaching this question. In this talk we will show how to use this strategy to study the problem in the two-dimensional case. To do so, we will introduce systolic-by-function complexes, which are a generalization of systolic complexes.