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Stefaan Vaes (KU Leuven)
Monday 26 June 2023, 10:00-11:00
Ergodic states on type III_1 factors and ergodic actions
- 👤 Speaker: Stefaan Vaes (KU Leuven)
- 📅 Date & Time: Monday 26 June 2023, 10:00 - 11:00
- 📍 Venue: Seminar Room 1, Newton Institute
Abstract
I will report on a joint work with Amine Marrakchi. Since the early days of Tomita-Takesaki theory, it is known that a von Neumann algebra that admits a state with trivial centralizer must be a type III 1 factor, but the converse remained open. I will present a solution of this problem, proving that such ergodic states form a dense G\delta set among all faithful normal states on any III _1 factor with separable predual. Through Connes’ Radon-Nikodym cocycle theorem, this problem is related to the existence of ergodic cocycle perturbations for outer group actions, which I will discuss in the second half of the talk.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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