Standard parabolic subgroup of Artin groups and their conjugation

by José Gálvez Mateos (Universidad de Sevilla)

Tuesday Oct 14, 2025, 4:00 PM → 5:00 PM Europe/Paris

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Artin groups are defined from a set of generators $S$ and relations $aba\cdots=bab\cdots$, where the words are of the same length. Objects of great interest within the study of these groups are the standard parabolic subgroups, which are the subgroups generated by a subset of the generators. In this talk, we will present a problem related to the conjugation of these subgroups known as the ribbon conjecture. It asks whether two parabolic subgroups $P$, $Q$, we have that $gPg^{-1}=Q$ if and only if $g$ is the product of an element of $P$ and some special elements called ribbons.