Speaker: Zhou Shuoxing (École normale supérieure)
Abstract: Given a tracial von Neumann algebra $(M,\tau)$, we prove that a state preserving $M$-bimodular ucp map between two stationary W$^*$-extensions of $(M,\tau)$ preserves the Furstenberg entropy if and only if it induces an isomorphism between the Radon-Nikodym factors. With a similar proof, we extend this result to quasi-factor maps between stationary spaces of locally compact groups and prove an entropy separation between unique stationary and amenable spaces. As applications, we use these results to establish rigidity phenomena for unique stationary Poisson boundaries. I will also talk about another application of the Radon-Nikodym factors, the Noncommutative Intermediate Factor Theorem, which is a recent joint work with Tattwamasi Amrutam and Yongle Jiang.
Time: 2025-09-05 15:30:00
Location: R1410, SIMIS
Introduction to the Speaker: Shuoxing Zhou is a PhD student in mathematics at the DMA, École normale supérieure, under the supervision of Prof. Cyril Houdayer. His research focuses on operator algebras, with a particular emphasis on von Neumann algebras. His work has been published in high-level journals such as the Journal of Functional Analysis and International Mathematics Research Notices.
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