The talk is related to a generalization of Katz' nilpotence conjecture to the irregular case. There are two relevant papers:
Holonomic D-modules and positive characteristic, Japan. J. Math. 4 , 1-25 (2009), e-print 1010.2908 where the conjecture is basically formulated, and its follow-up for some formal deformations of exponential-motivic D-Modules.
p-Determinants and monodromy of differential operators (with A.Odesskii), Selecta Mathematica (2022) 28:5, e-print 2009.12159.
In the second paper we have a very nice and unexpected result relating p-curvature and determinant of the logarithm of monodromy (notice the very unusual order of words: determinant of logarithm instead of logarithm of determinant!). The proof there is very convoluted. I have now a better simple proof which I can present in the talk, and a lot of new (semi)-experimental material, including generalization to q-difference equations.