Joint IAS/Princeton University Number Theory Seminar

This is an update on the talk I gave about 10 years ago on this seminar. The arithmetic Gan-Gross-Prasad (AGGP) conjecture, a high dimensional generalization of the Gross–Zagier theorem, relates the height pairing of arithmetic diagonal cycles on certain product Shimura varieties to the first central derivative of Rankin-Selberg tensor product L-functions. The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to the AGGP conjecture. I will recall the statement of the arithmetic fundamental lemma and present (a sketch of) a proof.​