Shuoxing Zhou: Rigidity of Furstenberg entropy under quasi-factor maps

mardi 7 oct. 2025, 09:45 → 11:45 Europe/Paris

Title: Rigidity of Furstenberg entropy under quasi-factor maps

Abstract: Given a locally compact second countable group $G$ and an admissible probability measure $\mu$ on $G$, we show that a quasi-factor map between two $(G,\mu)$-spaces preserves the Furstenberg entropy if and only if it induces an isomorphism between the Radon-Nikodym factors. I will also present the operator algebraic counterpart of this result for tracial von Neumann algebras. As a corollary, we prove an entropy separation between unique stationary and amenable spaces and apply it to establish rigidity phenomena for unique stationary Poisson boundaries. Finally, I will discuss another application of Radon–Nikodym factors, the Noncommutative Intermediate Factor Theorem, which is a recent joint work with Tattwamasi Amrutam and Yongle Jiang.