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30 - The ubiquitous hyperfinite II1 factor, 2019


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The ubiquitous hyperfinite II1 factor

Sorin Popa
Kyoto University / Distinguished Visiting Professor
University of California, Los Angeles / Professor

April 8, 9, 10, 11 and 12, 2019
110 Seminar Room Faculty of Science Bldg. #3 Kyoto University

Lecture Video

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 RM. 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.