A gold medal at the 2000 International Mathematical Olympiad marked the beginning of Xinyi Yuan’s trajectory in the field of mathematics. Since then, his focus has shifted toward arithmetic geometry, number theory, and automorphic forms, leading to significant theoretical advancements that characterize his current research profile as a professor at Peking University.
Academic Foundation
Born in 1981 in Huanggang, Hubei province, Yuan attended Huanggang Middle School before pursuing higher education at Peking University, where he earned an A.B. in mathematics in 2003. in 2008 under the supervision of Shou-Wu Zhang. Following his doctoral work, he held positions at the Institute for Advanced Study, Harvard University, and Princeton University, eventually securing a faculty role at the University of California, Berkeley, in 2012.
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Yuan's research includes the generalization of the equidistribution theorem developed by Lucien Szpiro, Emmanuel Ullmo, and Shou-Wu Zhang. In his 2008 paper published in Inventiones Mathematicae, he established conditions for the equidistribution of orbits under the absolute Galois group. Collaborating with Shou-Wu Zhang, he proved the averaged Colmez conjecture, which provided a foundation for Jacob Tsimerman’s later validation of the André–Oort conjecture for Siegel modular varieties. His work with Zhang also extended the theory of adelic line bundles to quasi-projective varieties, facilitating a reproof of the uniform Bogomolov conjecture.
Research on Rational Points
The study of Diophantine geometry remains central to Yuan's output. Working with Jiawei Yu and Shengxuan Zhou, he produced explicit uniform estimates for the count of rational points on curves of genus at least two, specifically linking these estimates to the Jacobian rank. In partnership with Junyi Xie, he investigated function fields, establishing proofs for the geometric Bogomolov conjecture in arbitrary characteristic and the geometric Bombieri-Lang conjecture for ramified covers of abelian varieties.
Professional Recognition
Yuan served as a Clay Research Fellow from 2008 to 2013. In 2020, he transitioned from the University of California, Berkeley, to a full professorship at Peking University. His recognition within the field culminated in being awarded the ICCM Gold medal at the 2025 International Congress of Chinese Mathematicians. Additionally, he was selected as an invited speaker for the 2026 International Congress of Mathematicians, reflecting his continued influence in arithmetic geometry and automorphic forms.
Fast facts
- Born: 1981, Huanggang
- Citizenship: People's Republic of China
- Ph.D. Institution: Columbia University
- Doctoral Advisor: Shou-Wu Zhang
- Primary Field: Applied Mathematics
- ICCM Gold Medal Year: 2025
- Former Faculty Position: University of California, Berkeley
Questions readers ask
What is Xinyi Yuan's primary area of research?
He works in number theory, arithmetic geometry, and automorphic forms, with a focus on Diophantine equations and L-functions.
Where did Yuan earn his doctoral degree?
He received his Ph.D. in mathematics from Columbia University in 2008.
Achievements
- Held posts at University of California, Berkeley
