Title: Bound on the number of rational points on curves

Speaker: Prof. Ziyang Gao (CNRS)

Time: 16:00-17:00, July 9, 2020 (Beijing Time)

Abstract: Mazur conjectured, after Faltings's proof of the Mordell conjecture, that the number of rational points on a curve depends only on the genus, the degree of the number field and the Mordell-Weil rank. This conjecture was established in a few cases. In this talk I will explain how to prove this conjecture and some of its generalization. I will focus on how functional transcendence and unlikely intersections on mixed Shimura varieties are applied. This is joint work with Vesselin Dimitrov and Philipp Habegger.