A Quantitative Version of the Uniform Mordell Conjecture

Explore a mathematical lecture presenting an explicit version of the uniform upper bound for rational points on curves of genus greater than one. Delve into the quantitative aspects of the celebrated Mordell conjecture, which was proven by Faltings and establishes that curves of genus greater than one over number fields have only finitely many rational points. Learn how deep uniform upper bounds emerge from Vojta's inequality and recent breakthrough work by Dimitrov-Gao-Habegger and Kuhne. Discover the explicit formulation of these uniform bounds through collaborative research with Jiawei Yu and Shengxuan Zhou. Gain insights into advanced topics in arithmetic geometry, Diophantine equations, and the intersection of algebraic geometry with number theory. Examine the technical methods used to make abstract existence results concrete and computable, bridging theoretical foundations with practical applications in understanding rational solutions to algebraic equations.