# Kyoto Operator Algebra Seminar

Organizers: Benoit COLLINS, Masaki IZUMI, Narutaka OZAWA.
Time and Location: 15:00 - 16:30 on Tuesday at RIMS 206
Seminar Description: This seminar features both research and introductory talks on topics in Operator Algebra, Noncommutative Geometry, Ergodic Theory, and Group Theory of various kinds (geometric, measure theoretic, functional analytic, etc.). The talks are informal and take between an hour and an hour and a half.
Useful Tips: How to Give a Good Colloquium. Advice on Giving Talks (Upgrade). Myths.
Memento: 2011  2012  2013  2014  2015

## 2016 Spring/Summer

 Mar. 28 - Apr. 04 RIMS 420 KTGU-IMU Mathematics Colloquia and Seminars May 17 14:00 - 15:30 RIMS 206 Hiroshi Ando (Chiba) Unitarizability, Maurey-Nikishin factorization and Polish groups of finite type In the seminal work of cocylcle superrigidity theorem, Sorin Popa introduced the class of finite type Polish groups. A Polish group $G$ is of finite type, if it is embeddable into the unitary group of a separable II$_1$ factor equipped with the strong operator topology. Popa proposed a problem of finding abstract characterization of finite type Polish groups. As Popa pointed out, there are two conditions which are clearly necessary for a Polish group $G$ to be of finite type, namely that (a) $G$ is unitarily representable (i.e., $G$ is embeddable into the full unitary group of $\ell^2$) and (b) $G$ is SIN, i.e., $G$ admits a two-sided invariant metric compatible with the topology. Popa asked whether these two conditions are actually sufficient. In 2011, Yasumichi Matsuzawa and I obtained several partial positive answers for some classes of Polish groups. In this talk, we show that there exists a unitarily representable SIN Polish group which is not of finite type, answering the above question. Our analysis is based on the Maurey-Nikishin Theorem on bounded maps from a Banach space of Rademacher type 2 to the space of all measurable maps on a probability space. This is joint work with Yasumichi Matsuzawa, Andreas Thom, and Asger Törnquist. May 30 - June 03 RIMS 420 Geometric Analysis on Discrete Groups Sep. 12-14 RIMS 420 Recent developments in operator algebras (program)

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