|Mar. 28 - Apr. 04||RIMS 420||KTGU-IMU Mathematics Colloquia and Seminars|
|May 17|| 14:00 - 15:30
| 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 $\ell^2$)
(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|
|Jne 10|| 14:00 - 15:30
| Yusuke Isono (RIMS)
Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We particularly prove a spectral gap rigidity result for the crossed products and, using recent results of Boutonnet-Ioana-Salehi Golsefidy, we provide examples of group measure space type III factors with no central sequences. This is joint work with C. Houdayer.
|Sep. 12-14||RIMS 420||Recent developments in operator algebras (program)|