in this talk, we consider a conjecture by gross and kudla that relates the derivatives of triple-product l-functions  for three modular forms and the height pairing of the gross—schoen cycles on shimura curves.

then, we sketch a proof of a generalization of this conjecture for hilbert modular forms in the spherical case. this is a report of work in progress with xinyi yuan and wei zhang, with help from yifeng liu.