Can there be a polymath project for mathematical physics? My hunch is that it might be possible to create something like https://polymathprojects.org/ for mathematical physics and I'd like to know whether MathOverflow users can recommend some appropriate problems. As Abdelmalek Abdessalam pointed out in the comments below such a platform can potentially be used to develop research programs in mathematical physics that are suitable for polymath type collaborative work.
The gist of this project would be to use collaborate problem-solving to tackle open problems in mathematical physics. Timothy Gowers wrote a seminal blog post on the subject here: Is massively collaborative mathematics possible?
There's a good point made by a commenter below as to why not simply use the current polymath platform. Well, I think that it would be easier for such a platform to succeed and gain support among mathematical physicists if it was maintained by mathematical physicists and focused mainly on problems in the area of mathematical physics. This is not the current setup of the Polymath project. 
 A: Polymath 7 tackled the hot spots conjecture(due to Jeffrey Rauch) in 2012: 

Suppose a flat piece of metal, represented by a two-dimensional
  bounded connected domain, is given an initial heat distribution which
  then flows throughout the metal. Assuming the metal is insulated (i.e.
  no heat escapes from the piece of metal), then given enough time, the
  hottest point on the metal will lie on its boundary.

The goal of the project was to establish the conjecture for a large range of triangles and partial results were documented on the blog. I must note that the associated wiki page is also very useful as it lists different cases as well as different approaches. 
I think this is a nice example of a non-trivial problem that can potentially be tackled on a collaborative problem solving platform focused on mathematical physics. 
A: I recommend the following problem :
Proof the existence of the spectral gap for the fractional quantum Hall effect at least for a simplified model where Laughlin's wavefunction is the exact ground state.
A: Many problems in the IQOQI list of open quantum problems have a strong aspect of mathematical physics, these could be of interest for such possible project.
Addendum: The question of OP was "I'd like to know whether MathOverflow users can recommend some appropriate problems." My answer does that, similar to the answer of user jjcale above.
