Abstract:

The holographic principle states that in the limit of a large number of degrees of freedom, some quantum systems give rise to an emergent gravitational spacetime with one more dimension. What are these quantum systems, and which properties must they have? In this talk, I will introduce the theory of von Neumann algebras as a natural language to explore this question. In particular, I will explain how these algebras allow to draw a precise connection between the emergence of a holographic causal structure and the ergodic properties of a many-body quantum system.