The p-curvature conjecture in families

The p-curvature conjecture is an analogue of the Hasse principle for arithmetic differential equations. I will discuss this conjecture in the context of families of algebraic varieties, and among other things, demonstrate a proof of the p-curvature conjecture for rank 2 vector bundles on generic curves. This is based on joint work with Anand Patel and Junho Peter Whang.​