Rigidity in Graphs of Groups

Explore rigidity problems in geometric group theory through a lecture by Emily Stark on rigidity in graphs of groups. Delve into the question of whether finitely generated groups sharing geometric structures also share algebraic structures. Examine cases where groups are quasi-isometric or act geometrically on the same proper metric space, and investigate if they are virtually isomorphic. Learn about the work of Papasoglu–Whyte on the quasi-isometric flexibility of infinite-ended groups, and discover new findings that demonstrate rigidity when assuming a common geometric model. Understand the concept of graphical discreteness and its application in proving rigidity results for various graphs of groups with graphically discrete vertex groups. Study action rigidity in free products of graphically discrete groups and quasi-isometric rigidity in amalgamated free products of closed hyperbolic 3-manifold groups over quasi-convex, almost malnormal nonabelian free subgroups. Gain insights from this joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse, presented as part of the Workshop on Geometry of Subgroups at the Centre de recherches mathématiques.