"All the three components (A, B and C above) of the project are complete. Our results are compiled within two preprints.
The first of these is entitled “p-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou”, we compete the tasks B and C above. This preprint is joint with Robert Pollack and Shu Sasaki. It is posted on ArXiv with identifier 1811.08216.
The goals of component A (construction of universal Heegner cycles) has been achieved in our preprint with Antonio Lei entitled ""Interpolation of Generalized Heegner Cycles in Coleman Families"". It is posted on ArXiv with identifier 1907.04086.
PI was also invited to address in important gatherings: “Iwasawa 2017” in Tokyo, “p-adic L-functions and algebraic cycles” in Taipei, “Special Cycles on Shimura Varieties and Iwasawa Theory” in Lausanne, “Stark's Conjectures, Iwasawa theory and related topics” in Exeter, ""Journees Arithmetiques"" in Istanbul and “Recent advances in the arithmetic of Galois representations” in Genoa. PI visited important mathematical centers; among others, he was invited to Bonn, Essen, London, Munich, Columbia U., Harvard U., MIT, Stanford U. and U. of Washington to speak at the local number theory seminars.
The dissemination activities the PI carried out within this action were not limited to scientific talks he delivered. He gave an instructional lecture series in Sofia University in Tokyo, he had regular mathematical exchange with Chi-Yun Hsu (a student of B. Mazur at Harvard) and he organized one of the problem sessions in the Arizona Winter School 2018.
In summary, the scientific portion of the action is complete. The PI worked hard to fulfill the dissemination goals of the action: He participated in 8 conferences/workshops (as an invited speaker in 7 of these), delivered 16 seminar talks in three continents and was invited to organize 2 instructional lecture series. We organized a satellite conference to Journees Arithmetiques XXXI in Istanbul, entitled ""p-adic modular forms""."
