I will consider the quantum connection of symplectic resolutions, which is of interest in representation theory and more recently in symplectic topology. I will explain its relationship in positive characteristic with the quantum Steenrod power operations of Fukaya and Wilkins. The relationship provides a geometric understanding of the p-curvature of such connections, while also allowing new computations for quantum Steenrod operations, including the case of the Springer resolution.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/12424