Top Global Course Special Lectures by Prof. Sorin Popa

Top Global Course Special Lectures by Prof. Sorin Popa (Kyoto University / UCLA) will take place as follows:

Course Title
Top Global Course Special Lectures 1
Date & Time
April 8 to 12, 2019
  • Monday, April 8, 15:00-17:00
  • Tuesday, April 9, 15:00-17:00
  • Wednesday, April 10, 13:00-15:00
  • Thursday, April 11, 15:00-17:00
  • Friday, April 12, 15:00-17:00
110 Seminar room, Faculty of Science Bldg. #3, Kyoto University
The ubiquitous hyperfinite II$_1$ factor
The hyperfinite ${\rm II}_1$ factor $R$ has played a central role in operator algebras ever since Murray and von Neumann introduced it, some 75 years ago. It is the unique amenable ${\rm II}_1$ factor (Connes 1976), and in some sense the smallest, as it can be embedded in multiple ways in any other ${\rm II}_1$ factor $M$. Many problems in operator algebras could be solved by constructing ''ergodic'' such embeddings $R \hookrightarrow M$. I will revisit such results and applications, through a new perspective, which emphasizes the decomposition $M$ as a Hilbert bimodule over $R$. I will prove that any ${\rm II}_1$ factor $M$ admits coarse embeddings of $R$, where the orthocomplement of $R$ in $M$ is a multiple of $L^2(R) \,\overline{\otimes}\, L^2(R^{\rm op})$. I will also prove that in certain situations, $M$ admits tight embeddings of $R$. Finally, I will revisit some well known open problems, and propose some new ones, through this perspective.
This series of lectures will be video-recorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.