=====Welcome=====

Welcome to the MIP* Resource page. Here is a collection of resources that may be helpful for those interested in understanding the [[https://arxiv.org/abs/2001.04383|MIP* = RE result]].

  * A high level [[https://quantumfrontiers.com/2020/03/01/the-shape-of-mip-re/|blog post]] that introduces the connection between MIP* = RE, Tsirelson's problem, and Connes' Embedding Conjecture. 
  * [[https://docs.google.com/document/d/1v0He_GTQcermi8v_8YBGVXTKUsQKec_6i5-EkApsK64/edit?usp=sharing|Here]] is a guide for people who are interested in starting a reading group around the MIP* = RE result, including its connections to the Connes' Embedding Problem. This includes suggestions for background reading.

=====Videos=====

  * [[https://www.birs.ca/events/2019/5-day-workshops/19w5163|Many Faceted Connes Embedding Problem]] workshop at Banff International Research Station. Speakers: various.
  * [[https://www.youtube.com/watch?v=Hkq8MwISUD4&feature=youtu.be&t=14524|How to compress a nonlocal game]]. Speaker: Henry Yuen. Gives an overview of the compression scheme used in MIP* = RE.
  * [[https://www.youtube.com/watch?v=pO-mzsZuCYo|Self-testing as an approach to certifying quantum systems]]. Speaker: Andrea Coladangelo. Gives an overview of nonlocal game rigidity/self-testing.
  * [[https://simons.berkeley.edu/talks/tbd-147|The algebraic side of MIP*=RE]]. Speaker: William Slofstra. Gives an algebraic viewpoint of the connection between CEP and MIP* = RE.
  * [[https://simons.berkeley.edu/talks/tbd-140|The Quantum Low-Degree Test]]. Speaker: Anand Natarajan. Gives an introduction to the robust self-testing result that underlies the introspection technique.
  * [[https://simons.berkeley.edu/talks/tbd-139|PCPs and Introspection]]. Speaker: John Wright. Gives an overview of the introspection technique.
  * [[https://www.youtube.com/watch?v=8Cmw5u8fazk|Spooky Complexity at a Distance]]. Speaker: Zhengfeng Ji. Gives an overview of MIP* = RE in the context of quantum multiprover interactive proofs.

=====Discussion Forum====
There's a [[http://piazza.com/utoronto.ca/summer2020/mipre|Piazza forum]] for those who may have questions about MIP* = RE or related topics. Sign up code: "quantum".

=====Reading Groups=====
Please contact me (Henry Yuen) if you'd like your reading group to be included on this list.

  * [[https://math.berkeley.edu/~ilc/events/cepmipre/|UC Berkeley reading group]], organized by Ian Charlesworth. Videos included.
  * [[http://perso.ens-lyon.fr/mikael.de.la.salle/GDT/GDT_Connes_Tsirelson.html.en|Reading webinar]], organized by Omar Fawzi, Mikael de la Salle, and Guillaume Aubrun. Slides and notes included.

=====Open Problems=====

  - Construct a [[hyperlinear|non-hyperlinear group]]. 
  - What is the most general class of question distributions that can be [[introspection|introspected]]? 
  - What is the complexity of MIP<sup>co</sup>, or equivalently, the complexity of approximating the commuting operator value of nonlocal games? A plausible conjecture is that it is equal to [[core|coRE]].

More to come. Also, please feel free to suggest more open problems (either by e-mail, or on the Piazza forum).