Jill Mastrocola, Brandeis University
2023 AWM Research Symposium
Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]

Parabolic subgroups are an important tool for studying the properties of Artin groups. One fundamental question is whether the intersection of a set of parabolic subgroups is itself a parabolic subgroup. This question is open in the general case, but is known to be true for many subclasses of Artin groups, including braid groups, right-angled Artin groups, and Artin groups of spherical type. Recent progress has been made in the case of large-type Artin groups, and we look to extend these results.

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