This MO question "Property $\Gamma$ in terms of correspondences" led us to answer two old open problems and to push further a third more recent result:
Jon Bannon, Amine Marrakchi, Narutaka Ozawa. Full factors and co-amenable inclusions, arxiv/1903.05395.
Ilya Bogdanov has answered my question Graphs with only disjoint perfect matchings
on certain coloring in graphs, that emerged through research in quantum physics. This answer has inspired quite a bit of research:
Quantum Experiments and Graphs (arXiv - cited Bogdanov's MO answer)
Quantum experiments and graphs II (arXiv)
Quantum experiments and graphs. ...