Appears in collection : Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

The celebrated Mordell conjecture proved by Faltings asserts that the number of rational points on a curve of genus greater than one over a number field is finite. A deep uniform upper bound on the number of rational points follows from Vojta's inequality and the recent works of Dimitrov-Gao-Habegger and Kuhne. In this talk, I will introduce an explicit version of this uniform bound. This is a joint work with Jiawei Yu and Shengxuan Zhou.