Lesson plan

Connes embedding problem

Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several different areas of mathematics. Dan Voiculescu developing his free entropy theory found that Connes' embedding problem is related to the existence of microstates. Some results of von Neumann algebra theory can be obtained assuming positive solution to the problem. The problem is connected to some basic questions in quantum theory, which led to the realization that it also has important implications in computer science. The problem admits a number of equivalent formulations. Notably, it is equivalent to the following long-standing problems: * Kirchberg's QWEP conjecture in C*-algebra theory * Tsirelson's problem in quantum information theory * The predual of any (separable) von Neumann algebra is finitely representable in the trace class. In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problem. However, an error was discovered in September 2020 in an earlier result they used; a new proof avoiding the earlier result was published as a preprint in September.…

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Article summary

Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several different areas of mathematics. Dan Voiculescu developing his free entropy theory found that Connes' embedding problem is related to the existence of microstates. Some results of von Neumann algebra theory can be obtained assuming positive solution to the problem. The problem is connected to some basic questions in quantum theory, which led to the realization that it also has important implications in computer science. The problem admits a number of equivalent formulations. Notably, it is equivalent to the following long-standing problems: * Kirchberg's QWEP conjecture in C*-algebra theory * Tsirelson's problem in quantum information theory * The predual of any (separable) von Neumann algebra is finitely representable in the trace class. In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen announced a result in quantum complexity theory that implies a negative answer to Connes' embedding problem. However, an error was discovered in September 2020 in an earlier result they used; a new proof avoiding the earlier result was published as a preprint in September.…

Key claims

  1. publication date: 2021 — source: Wikipedia · confidence 0.95

Discussion questions

  1. Summarise the article in your own words. Which single claim would you verify first, and why?
  2. The record states that the publication date is "2021". What evidence would count against this claim?
  3. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
  4. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

  1. Wikipedia https://en.wikipedia.org/w/index.php?oldid=1370392131

Key claims and bibliography are generated from the same tracked claims and sources as the article page.