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 ...

Arithmetic geometry and Diophantine geometry lie at the confluence of number theory and algebraic geometry, exploring the deep connections between the arithmetic properties of numbers and the ...

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 ...

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 ...