Connes Embedding Problem

### What is the conjecture
Connes' embedding problem asks whether every [type II1 factor](https://en.wikipedia.org/wiki/Von_Neumann_algebra) on a separable [Hilbert space](https://en.wikipedia.org/wiki/Hilbert_space) can be embedded into some $R^{\omega}$. See more information at https://en.wikipedia.org/wiki/Connes_embedding_problem.

### Prerequisites needed
Requires a lot of infrastructure to be built in mathlib.

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-08

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

The issue names no file, test, or entry point. Begin by assessing the stated mathlib infrastructure prerequisites; completion is a formalized Connes Embedding Problem added to the repository.

Written by the indexing model from the issue text.