Title: 
Furstenberg's Boundary Theories: Construct one, get one free.

Abstract: 
During the 60s and the 70s, Furstenberg developed two parallel theories regarding a group's boundaries of different flavours. One is topological, known nowadays as the Furstenberg boundary, and the other is measurable and relates to random walks, called the Furstenberg-Poisson boundary. Both have universal properties (injectivity\Zimmer amenability), and so, their structure reveals various groups' properties. The research of these two theories and their connections with Operator Algebra theory and rigidity of higher rank lattices is still very active, yet many questions are open.
These theories are known to share some common components, but the reason for that is not apparent. I'll argue that the reason is that they share the same driving force. We will develop one categorical machinery to produce them both simultaneously, despite their differences—two Boundary Theories for the price of one.

Recording/Livestream: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=381a08a8-312b-4097-82a4-b1b500624eb6