Groups and Dynamics Seminar

During the 60s and the 70s, Furstenberg developed two parallel theories regarding a group's boundaries of different flavours: the Furstenberg boundary and the Furstenberg-Poisson boundary. Both have universal properties (injectivity\Zimmer amenability) and so, their structure reveals certain groups' properties. It is no surprise that the research of these two theories and their connections with Operator Algebra Theory and rigidity phenomena of higher-rank lattices is still very active. These theories are known to share some common components, but the reason for that is not so apparent. I'll argue that the reason is that they share the same driving force, potentially suggesting direct connections between these objects. We will develop one categorical machinery to produce them both simultaneously, despite their different nature - two Boundary Theories for the price of one! Joint with Mehrdad Kalantar.