Xinyi Yuan (; born 1981) is a Chinese mathematician who is currently a professor of mathematics at Peking University working in number theory, arithmetic geometry, and automorphic forms. In particular, his work focuses on arithmetic intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions.
Early life and education Yuan is from Macheng, Huanggang, Hubei province, and graduated from Huanggang Middle School in 2000. That year, he received a gold medal at the International Mathematical Olympiad while representing China."Xinyi Yuan – Official IMO Results", International Mathematical Olympiad. Retrieved on 4 December 2016. Yuan obtained his A.B. in mathematics from Peking University in 2003 and his Ph.D. in mathematics from the Columbia University in 2008 under the direction of Shou-Wu Zhang."Xinyi Yuan CV", UC Berkeley. Retrieved on 3 December 2016. His article "Big Line Bundles over Arithmetic Varieties," published in Inventiones Mathematicae, demonstrates a natural sufficient condition for when the orbit under the absolute Galois group is equidistributed.
Career He spent time at the Institute for Advanced Study, Princeton University, and Harvard University before joining the Berkeley faculty in 2012."IAS Member – Xinyi Yuan", Institute for Advanced Study. Retrieved on 4 December 2016.
Yuan was appointed a Clay Research Fellow for a three-year term from 2008 to 2013."Xinyi Yuan", Clay Mathematics Institute. Retrieved on 3 December 2016. Together with a number of other collaborators, Yuan was profiled in Quanta Magazine and Business Insider for, among other things, his research on L-functions."Math Quartet Joins Forces on Unified Theory", Quanta Magazine. Retrieved on 3 December 2016."Math Quartet Joins Forces on Unified Theory", Business Insider. Retrieved on 4 December 2016.
Yuan left UC Berkeley to become a full professor at Peking University in 2020. In 2025, Yuan was award the ICCM Gold medal at the International Congress of Chinese Mathematicians.https://iccm.simis.cn/iccm2025/site/awards/medal-of-mathematics/ . Retrieved on 25 May 2026. He is also an invited speaker at the 2026 International Congress of Mathematicians.https://www.icm2026.org/event/ac193975-5d24-4628-8c30-ddb23de19a8b/speakers. Retrieved on 25 May 2026.
Research In his thesis, Yuan generalized the equidistribution theorem of Lucien Szpiro, Emmanuel Ullmo and Shou-Wu Zhang to the broader framework of adelic line bundles and in particular to algebraic dynamical systems. Together with Shou-Wu Zhang, Yuan proved the averaged Colmez conjecture which was later shown to imply the André–Oort conjecture for Siegel modular varieties by Jacob Tsimerman.
With Shou-Wu Zhang, Yuan wrote a monograph generalizing the theory of adelic line bundles to quasi-projective varieties. Yuan subsequently applied these ideas to reprove the uniform Bogomolov conjecture for curves, thereby obtaining a new proof of Mazur's Conjecture B. Later, in collaboration with Jiawei Yu and Shengxuan Zhou, he derived the first explicit uniform estimate for the number of rational points on curves of genus at least two in terms only of the Jacobian rank.
Yuan has also made major contributions to Diophantine geometry over function fields through joint work with Junyi Xie. Their results include proofs of the geometric Bogomolov conjecture in arbitrary characteristic and the geometric Bombieri-Lang conjecture for ramified covers of abelian varieties.
Publications (selected)
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