Hiroki Sako @ RIMS, Kyoto

Research Fellow of the Japan Society for the Promotion of Science (JSPS Research Fellow)
Research Institute for Mathematical Sciences (RIMS)
Kyoto University
Kyoto University, Kyoto 606-8502, Japan

Email: sako [_at_] kurims.kyoto-u.ac.jp
Room: Maskawa building for education and research room 501

[4] H. Sako, Property A and the operator norm localization property for discrete metric spaces,
preprint, arXiv:1203.5496.
abstract

We study property A defined by G. Yu and the operator norm localization property defined by X. Chen, R. Tessera, X. Wang, and G. Yu. These are coarse geometric properties for metric spaces which have applications to operator K-theory. It is proved that the two properties are equivalent for discrete metric spaces with bounded geometry. In the revised version, we make comments on a coarse geometric properties defined by Brodzki, Niblo, Spakula, Willett, and Wright

[3] H. Sako, Concrete Classification and Centralizers of Certain $\mathbb{Z}^2 \rtimes SL(2, \mathbb{Z})$-actions,
J. Math. Soc. Japan, 62 (2010), no.1, 135--166. arXiv:0704.1533.
abstract

We introduce a new class of actions of the group $\mathbb{Z}^2 \rtimes SL(2, \mathbb{Z})$ on finite von Neumann algebras and call them twisted Bernoulli shift actions. We classify these actions up to conjugacy and give an explicit description of their centralizers. We also distinguish many of those actions on the AFD $\mathrm{II}_1$ factor in view of outer conjugacy.

We get three types of results on measure equivalence rigidity; direct product groups of Ozawa's class $\mathcal{S}$ groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct product groups of Ozawa's class $\mathcal{S}$ groups. As consequences, Monod--Shalom type orbit equivalence rigidity theorems follow. We prove that if two wreath product groups $A \wr G$, $B \wr \Gamma$ of non-amenable exact direct product groups $G$, $\Gamma$ with amenable bases $A$, $B$ are measure equivalent, then $G$ and $\Gamma$ are measure equivalent. We get Bass--Serre rigidity results on amalgamated free products of non-amenable exact direct product groups.

We prove that being in Ozawa's class $\mathcal{S}$ for countable discrete groups is invariant under measure equivalence. As a corollary, we show that if a countable group $G$ is measure equivalent to a free group, then the group von Neumann algebra $L(G)$ is solid.

Education:
April 2001 - March 2005 (Undergraduate), University of Tokyo
April 2005 - March 2007 (Master course), Graduate school of Mathematical Sciences, University of Tokyo
April 2007 - March 2009, Department of Mathematics, University of California Los Angeles (Adviser: Sorin Popa)
April 2007 - March 2010 (Doctoral course), Graduate school of Mathematical Sciences, University of Tokyo (Adviser: Yasuyuki Kawahigashi)
April 2010--March 2011, JSPS Research Fellow, Graduate school of Mathematical Sciences, University of Tokyo
April 2011--March 2013, JSPS Research Fellow, Research Institute for Mathematical Sciences, Kyoto University

Degree:
March 2005, B.Sc., University of Tokyo
March 2007, Master, Graduate School of Mathematical Sciences, University of Tokyo

Fellowship:
April 2007--March 2010, Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists (DC1)
April 2010--(March 2013), Research Fellow of the Japan Society for the Promotion of Science (PD)
Citizenship: Japan

Hiroki SAKO