A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

Diophantine geometry of algebraic curves explores the solutions of polynomial equations in integers or rational numbers by combining techniques from algebraic geometry, number theory and arithmetic ...

The set of solutions to a diophantine equation is strongly influenced by the geometry of the associated algebraic variety. This paradigm, for example, suggests that an elementary proof of Fermat’s ...

Hyperbolic geometry studies spaces of constant negative curvature, where the parallel postulate is replaced and geodesics exhibit exponential divergence. This framework underpins a rich theory of ...

Zheng Xiao received his PhD in 2022 at Michigan State University, under the supervision of Aaron D. Levin. His research interests include number theory, arithmetic geometry and complex hyperbolic ...