Xinjing Zhou

Ph.D XL

Research Project

Diophantine Geometry: Rational Points, Hyperbolicity, and the Betti Map

My research focuses on Diophantine Geometry, the study of integer and rational points on algebraic varieties through geometric methods. I will investigate fundamental conjectures in the field, such as Vojta’s, which link the distribution of these points to geometric invariants like the canonical bundle. The project also explores Hilbert’s irreducibility property beyond classical settings, and examines the interplay between algebraic, arithmetic, and complex-analytic aspects of hyperbolicity. A further goal is to advance the study of torsion points via sections of abelian schemes and the associated Betti map.