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, 15:0017:00
 Tuesday, April 9, 15:0017:00
 Wednesday, April 10, 13:0015:00
 Thursday, April 11, 15:0017:00
 Friday, April 12, 15:0017:00
 Venue
 110 Seminar room, Faculty of Science Bldg. #3, Kyoto University
 Title
 The ubiquitous hyperfinite II$_1$ factor
 Abstract
 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.
 Language
 English
 Note
 This series of lectures will be videorecorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.