in the 90s kollár proved non-rationality of many degrees and dimensions of complex fano hypersurfaces by considering their degenerations modulo p and taking advantage of the surprising existence and positivity of differential forms on their reductions. in a series of papers with chen, church, and ji, we have shown that these differential forms in characteristic p can give insight into many other aspects of the birational geometry of complex hypersurfaces: the degree of irrationality, rational endomorphisms, the birational automorphism group, and rational fibrations in low genus curves.