Median Spaces and Algebras - Part I

Explore the concept of median spaces and algebras in this comprehensive lecture from the Workshop on Cube Complexes and Combinatorial Geometry. Delve into the mathematical foundations of median spaces as a generalization of L^1 spaces, CAT(0) cube complexes, and R-trees. Discover their significance in geometric group theory, examining their applications in studying quasi-flats, quasi-isometries, and automorphisms for various group classes, including those with HHS structure and cocompactly cubulated groups. Investigate the role of infinite-dimensional median spaces and their dual concept, spaces with measured walls, in testing functional analytic properties such as Kazhdan's property (T) and the Haagerup property. Gain insights into the connections between median spaces and median algebras, and understand their implications for the study of cocompactly cubulated groups in this 47-minute presentation by Elia Fioravanti at the Centre de recherches mathématiques.