Xinyi Yuan

Scientific careerFieldsMathematicsInstitutionsPeking University
University of California, Berkeley
Institute for Advanced Study
Princeton University
Harvard UniversityThesis Equidistribution Theory over Algebraic Dynamical Systems  (2008)Doctoral advisorShou-Wu Zhang

Xinyi Yuan (Chinese: 袁新意; 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.^[1] In particular, his work focuses on arithmetic intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions.

Yuan is from Macheng, Huanggang, Hubei province, and graduated from Huanggang Middle School in 2000.^[2] That year, he received a gold medal at the International Mathematical Olympiad while representing China.^[3] 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.^[4] 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.^[5]

He spent time at the Institute for Advanced Study, Princeton University, and Harvard University before joining the Berkeley faculty in 2012.^[6]

Yuan was appointed a Clay Research Fellow for a three-year term from 2008 to 2013.^[7] 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.^[8][9]

Yuan left UC Berkeley to become a full professor at Peking University in 2020.^[10]

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.^[11][12]

• (with Tong Zhang) "Effective Bound of Linear Series on Arithmetic Surfaces", Duke Mathematical Journal 162 (2013), no. 10, 1723–1770.
• "On Volumes of Arithmetic Line Bundles", Compositio Mathematica 145 (2009), 1447–1464.
• "Big Line Bundles over Arithmetic Varieties", Inventiones mathematicae 173 (2008), no. 3, 603–649.
• (with Tong Zhang) "Relative Noether inequality on fibered surfaces", Advances in Mathematics 259 (2014), 89–115.
• (with Shou-Wu Zhang) "The arithmetic Hodge index theorem for adelic line bundles", Mathematische Annalen (2016), 1–49.
• (with Wei Zhang, Shou-Wu Zhang) "The Gross–Kohnen–Zagier theorem over totally real fields", Compositio Mathematica 145 (2009), no. 5, 1147–1162.
• (with Wei Zhang, Shou-Wu Zhang) "The Gross–Zagier formula on Shimura curves", Annals of Mathematics Studies vol. 184, Princeton University Press, 2012.
• (with Wei Zhang, Shou-Wu Zhang) "Triple product L-series and Gross–Kudla–Schoen cycles", preprint.
• Yuan, Xinyi; Zhang, Shou-Wu (2018). "On the averaged Colmez conjecture". Annals of Mathematics. 187 (2): 553–638. arXiv:1507.06903. doi:10.4007/annals.2018.187.2.4. S2CID 118916754.