Pure Maths Colloquium - Acylindrical hyperbolicity of graph products of groups - Motiejus Valiunas (Southampton) Seminar

Event details

Abstract: Graph products are a class of groups that interpolate between direct and free products, and include widely studied examples such as the right-angled Artin groups. It is known that most of such groups belong to the class of acylindrically hyperbolic groups, which also includes and shares many properties with (relatively) hyperbolic groups. A recent result suggests a relation between this class and the class of equationally noetherian groups: these are groups for which any system of equations has the same solution set as some finite subsystem. In this talk I will explicitly describe an action of a graph product on a space quasi-isometric to a tree, hence giving an alternative way to prove acylindrical hyperbolicity of graph products. As an application, I will outline how this action can be used to show that, under certain conditions, the property of being equationally noetherian is preserved under forming graph products.