L^2-Invariants and Dynamical Invariants in Algebraic Actions

L^2-Invariants and Dynamical Invariants in Algebraic Actions

Explore the connections between $L^2$-invariants theory and topological dynamical systems in this 48-minute lecture by Hanfeng Li at BIMSA. Delve into the study of numerical invariants for spaces with discrete group actions, including $L^2$-torsion and $L^2$-Betti numbers, using operator algebra tools. Examine continuous actions of countable discrete groups on compact metrizable spaces, focusing on entropy and mean dimension as key invariants. Discover how these invariants correspond to each other in the context of algebraic actions, bridging the gap between $L^2$-invariants theory and dynamical systems.