Date | 2021-10-06 |
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Speaker | Magdalena Musat |

Dept. | University of Copenhagen |

Room | 선택 |

Time | 16:00-18:00 |

**※ Zoom 회의 ID : 356 501 3138 / 암호 : 471247**

In his famous classification paper from 1976, Alain Connes suggested that it “ought to
be true” that all finite von Neumann algebras admit an approximate embedding into the so-called
hyperfinite type II_{1} factor R. One can replace the hyperfinite II_{1} factor by a matrix algebra, and so
the Connes Embedding Problem asks if any von Neumann algebra (or C^{*}-algebra) with a tracial
state can be approximated by matrix algebras, with respect to the norm arising from the trace. The
depth of this problem is witnessed by its many reformulations (and applications) in different areas
of mathematics, including group theory (Are all groups hyperlinear?, or sofic?) and later, via deep
theorems of Kirchberg, in quantum information theory (in the form of Tsirelson’s conjecture). Very
recently, a negative answer to the Connes Embedding Problem has been announced by Ji, Natarajan,
Vidick, Wright and Yuen in their 206 pages-long paper titled MIP^{*}=RE, using quantum complexity
theory. In this overview talk, I will explain some of the several facets of the Connes Embedding
Problem, with particular emphasis on the related interplay between operator algebras and quantum
information theory

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