I was talking with a number of physicists this evening, and of the papers who's problem statement we understood, I don't think any of them will have near-term applications. For most of them, they were results that I think the physics community believed to be true, and the paper provides the first rigorous proof. For several it was news to me that they weren't already theorems! These results are important advances in mathematical physics, but they don't tend to have much impact on experiment.
From what I can tell, all of the physics results here are quite mathematical. But I am very curious how the internal model they used would perform on more applied problems.