Sorin Popa教授 スーパーグローバルコース数学特別講義1

Sorin Popa教授(Kyoto University / UCLA)によるスーパーグローバルコース数学特別講義を下記の要領で行います。


スーパーグローバルコース 数学特別講義1
日 時
  • 4月 8日(月) 15:00〜17:00 (講義ノート
  • 4月 9日(火) 15:00〜17:00
  • 4月10日(水) 13:00〜15:00
  • 4月11日(木) 15:00〜17:00
  • 4月12日(金) 15:00〜17:00
場 所
京都大学理学部3号館 110講義室
題 目
The ubiquitous hyperfinite ${\rm II}_1$ factor
概 要
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.
言 語
備 考