The ubiquitous hyperfinite II1 factor

Lecture 1 Sorin POPA

Course Description
The hyperfinite II 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 II factor (Connes 1976), and in some sense the smallest, as it can be embedded in multiple ways in any other II factor M. Many problems in operator algebras could be solved by constructing ”ergodic” such embeddings R↪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 II factor Madmits coarse embeddings of R, where the orthocomplement of R in M is a multiple of L. 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.

講義詳細

年度・期
2019年度・前期集中
開催日
2019年4月08日 から 4月12日
開講部局名
理学研究科
使用言語
英語
教員/講師名
Sorin POPA(Distinguished Visiting Project Professor, Kyoto University / Professor, University of California, Los Angeles)
開催場所
110 Seminar Room, Faculty of Science Bldg No 3
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